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Andrew Potter*
Text as tautology: an exploration in
inference, transitivity, and logical
compression
https://doi.org/10.1515/text-2020-0230
Received December 29, 2020; accepted November 30, 2021; published online December 27, 2021
Abstract: Rhetorical structure theory (RST) and relational propositions have
been shown useful in analyzing texts as expressions in propositional logic.
Because these expressions are systematically derived, they may be expected
to model discursive reasoning as articulated in the text. If this is the case, it
would follow that logical operations performed on the expressions would be
reflected in the texts. In this paper the logic of relational propositions is used to
demonstrate the applicability of transitive inference to discourse. Starting with
a selection of RST analyses from the research literature, analyses of the logic of
relational propositions are performed to identify their corresponding logical
expressions and within each expression to identify the inference path implicit
within the text. By eliminating intermediary relational propositions, transi-
tivity is then used to progressively compress the expression. The resulting
compressions are applied to the corresponding texts and their compressed RST
analyses. The application of transitive inference to logical expressions results
in abridged texts that are intuitively coherent and logically compatible with
their originals. This indicates an underlying isomorphism between the infer-
ential structure of logical expressions and discursive coherence, and it con-
firms that these expressions function as logical models of the text. Potential
areas for application include knowledge representation, logic and argumen-
tation, and RST validation.
Keywords: coherence relations; discourse analysis; inference; propositional logic;
relational propositions; rhetorical structure theory
*Corresponding author: Andrew Potter, Department of Computer Science & Information Systems,
University of North Alabama, 236 Keller Hall, 35632, Florence, AL, USA, E-mail: apotter1@una.edu.
https://orcid.org/0000-0001-8866-4714
Text & Talk 2021; aop
1 Introduction
The relationship between language and logic has long been of interest to researchers
in pragmatics, semantics, philosophy, and related disciplines. Among the many
perspectives presented on this topic has been the notion that logic is, in one way or
another, an implicit property of discourse coherence (e.g., Asher and Lascarides
2003; Brandom 2000; Kamp and Reyle 1993; Peregrin 2014; Potts 2005). Of particular
interest here is the viewthat the combined application of rhetorical structure theory
(RST) and relational propositions, as defined by Mann and Thompson (1986, 1988),
can be used to analyze texts asexpressions in propositional logic (Potter 2018). That
these expressions tend to model established rules of inference gives rise to a curious
consequence. As logic textbooks (Copi 1972) readily inform us, rules of inference are
by definition tautologies. That is to say, they are logical expressions that hold irre-
spective ofthe truth values of their arguments.From thisit would follow that among
the properties of a coherent discourse will be that it is a tautology. If so, it should be
also the case that coherent discourses should survive treatment as such—that is,
inferences that may be drawn from their tautological analogs should be applicable
to the respective texts as well, with little to no loss of coherence.
In this paper, this logic of relational propositions is used to demonstrate the
applicability of transitive inference operations to written discourse. Transitivity is a
property of a logical expression through which Boolean, or deductive, values are
transmitted through an inferential chain. Using a set of analyses from the RST
literature, the logic of relational propositions is used to identify their corresponding
logical expressions, and for each expression the inference path. By eliminating
intermediary relational propositions from within the inference path, transitivity is
used to progressively compress the expression. The resulting compression is then
applied to the corresponding text.
If tautology is a property of a coherent discourse, then the application of tran-
sitive inference should result in abridged texts that would be intuitively coherent
and logical consequences of their originals, indicating the presence of underlying
isomorphisms between inferential structure and discursive coherence. And this in
turn would indicate that the expressions will function as logical models of the text,
enabling manipulation of discourse as such. This finding, that logical integrity is a
core feature of textual coherence would have significancefor research in a number of
disciplines including logic mining, argumentation studies, informal logic, discourse
analysis, natural language processing, and knowledge representation.
The paper is organized as follows: Section 2 provides a review of related
research, Section 3 describes the methodology used in this analysis, Section 4 pre-
sents the applications of the methodology to selected RST analyses, and Section 5
2Potter
concludes the paper with a discussion of the results and prospects for how the
methodology might be applied.
2 Literature review
Research concerning the relationship between coherence relations and logic has
been an active area of research at least since Hobbs (1979, 1985) used logic to define
a set of relations for use in an automated inference system and this has continued
in numerous other studies in the logic of coherence relations (e.g., Asher and
Lascarides 2003; Danlos 2008; González and Ribas 2008; Groenendijk 2009; Marcu
2000; Potter 2018, 2020; Sanders et al. 1992; Wong 1986).
Much recent research in this area has been influenced by the work of Asher and
Lascarides (2003), with their development of Segmented Discourse Representation
Theory (SDRT). SDRT is based in part on Discourse Representation Theory (DRT), a
theory of dynamic semantics that attempts to account for the context dependence
of meaning, arising from the observation that the way a sentence is interpreted
depends on what has occurred previously within the discourse (Kamp and Reyle
1993; Kamp et al. 2011). That is, the discourse context is dynamically modified with
each successive utterance, and this updated context informs the interpretation
of whatever comes next. SDRT uses DRT semantics to generate dynamic in-
terpretations of discourse. Updates consist in identifying appropriate rhetorical
relations for linking new information to old, assigning a compositional and dy-
namic semantic interpretation for the discourse. SDRT is designed in part to
address open issues in RST and other theories using coherence relations.
Asher and Lascarides (2003) cite earlier work from Moore and Pollack (1992),
which indicated ambiguities not only in relation identification but in nuclearity
as well. While Moore and Pollack regardedthisasaseriousproblemforRST,
Mann and Thompson (1987b, 1988) viewed simultaneous analyses as normal and
consistent with their theory. Asher and Lascarides argued that although texts
support both intentional and informational structures, reasoning about in-
tentions uses different rules from those needed for rhetorical relations, so that
intentional and discourse structures must be treated separately (Asher and
Lascarides 1994). Yet intentional structure is foundational for RST. As Mann and
Thompson (1988: 258) put it, “…the [RST] definitions are stated in terms of how
the text produces an effect on the reader which the writer could reasonably have
intended.”These effects are achieved through the relationship between satellite
and nuclear elements. That these relationships are inferential is fundamental to
the claims developed in this paper. In contrast with Asher and Lascarides, since
inferences are based on intended effect, they are indefeasible. When a text
Text as tautology 3
incorporates an expression of defeasibility, the defeasibility is part of the
intended effect. Any hedging, uncertainty, or other qualifications are integral to
the inferential structure. When a text provides no indication of defeasibility, if
the reader regards the inference as less than assured, this indicates a discrepancy
between intended and realized effect. The treatment of defeasibility is given
further consideration in Section 4.3.
The possibility of an inferential substructure to RST has been proposed in a few
earlier works. Wærn and Ramberg (2004) proposed a system that would use RST to
constructexplanation networksintegrated with Toulmin’s(1958)modeltofind paths
through these networks, resulting in a dual level knowledge system that would
support inferencing and explanation derivation. Building on this, Potter (2007, 2010)
described an approach to explanation-aware knowledge representation that would
use a reasoning model that could be applied to support intelligent human-computer
collaboration and controlled natural languages. Potter (2018) showed how RST
could be used to define a method for rendering and analyzing texts as expressions in
propositional logic. This provides the foundation for the current work.
3 Methodology and analytical procedure
The methodology used here consists of five sequentially applied steps:
1) Analyze the text using RST;
2) Restate the RST analysis as a relational proposition;
3) Render the relational proposition as an expression in propositional logic;
4) Apply transitivity to the logical expression, yielding a compressed expression;
and
5) Apply the same compression to the text and assess the result.
Each step leverages a well-defined conceptual framework: rhetorical structure theory
(Mann and Thompson 1988), relational propositions (Mann and Thompson 1986), the
logicofrelationalpropositions(Potter2018),andlogicaltransitivity(Copi1967).
The first step is to analyze the text using rhetorical structure theory. RST
defines discourse coherence in terms of the relations that hold between parts of the
text. An RST relation consists of a satellite, a nucleus, and a relation. The relation
holds between the satellite and nucleus. The satellite and nucleus are either
elementary discourse units (usually a clause) or substructures consisting of lower
level RST relations. The distinction between satellite and nucleus arises as a result
of the rhetorical asymmetry of relations. Within a relation, the nucleus is more
salient than the satellite. The result of an RST analysis is a tree structure of satellite-
nuclei relations, such as the one shown in Figure 1. Since the RST analyses used in
4Potter
this paper are from the existing studies, this first step is reduced to selecting
appropriate examples. The analyses used are from published articles on RST. A
listing of these articles may be found in Appendix.
The second step is to restate the RST analysis as a relational proposition. The
theory of relational propositions is an alternative conceptualization of RST, such that
the relations between satellites and nuclei are treated as implicit coherence-
producing assertions (Mann and Thompson 1986). A relational proposition consists
of a predicate and a pair of arguments. The predicate corresponds to the RST rela-
tion, and the arguments correspond to its satellite and nucleus. For example, using
the predicate notation defined by Potter (2018), the relational proposition for the
CIRCUMSTANCE relation from Figure 1 is circumstance(3,2), and the nested relational
propositions corresponding to the entire structure shown in Figure 1 is as follows:
background(
volitionalResult(
1,
circumstance(
3,2)),
evidence(
concession(
5,
antithesis(
7,6)),4))
Figure 1: Not Laziness RST analysis (Mann and Thompson 1988).
Text as tautology 5
Relational propositions may be treated as truth-functional assertions. The
relational proposition circumstance(3,2) holds insofar as it achieves its intended
effect, namely that the satellite provides an enabling context for its nucleus. Nested
relational propositions specify hierarchies of intentional effects, wherein de-
pendencies flow upward from the elementary units to the central locus of effect.
The third step is to render the relational proposition as an expression in
propositional logic. The logic of relational propositions enables specification of
relational propositions as logical expressions (Potter 2018). For each relation there
is a corresponding logical form. For example, in the EVIDENCE relation the satellite
provides evidence in support of the nucleus. The reader recognizes the implicative
relationship between the satellite and the nucleus, with the result that the reader’s
belief in the nucleus is increased upon comprehension of this relationship.
Without this evidence, the reader may not believe the nucleus. In argumentative
terms, the satellite is the ground and the nucleus is the claim. Logically, the
satellite is the antecedent and the nucleus is the consequent. Thus, EVIDENCE im-
plements the modus ponens rule of inference: (((s /n) ∧s) /n), where sis the
satellite and nis the nucleus. The logical forms for many relations implement rules
of inference, hence are logically valid arguments. This is a consequence of the
realization of intended effect. Table 1 provides a summary of the logical definitions
for the RST relations used in this paper (For a detailed discussion of these defi-
nitions see Potter [2018]).
Just as relational propositions are nested to reflect their position within an RST
tree, logical expressions may be nested within one another. From this perspective,
an RST analysis is a recursive tree of logical expressions. These expressions can be
complex. For example, the logical expression for the Not Laziness analysis
(Figure 1) is as follows:
((((((1 /(((3 /2) ∧3) /2)) ∧1) /(((3 /2) ∧3) /2)) /((((((¬(5 /¬(((7 ∨6) ∧¬7) /
6)) /(((7 ∨6) ∧¬7) /6)) ∧¬(5 /¬(((7 ∨6) ∧¬7) /6))) /(((7 ∨6) ∧¬7) /6)) /4) ∧
(((¬(5 /¬(((7 ∨6) ∧¬7) /6)) /(((7 ∨6) ∧¬7) /6)) ∧¬(5 /¬(((7 ∨6) ∧¬7) /6))) /
(((7 ∨6) ∧¬7) /6))) /4)) ∧(((1 /(((3 /2) ∧3) /2)) ∧1) /(((3 /2) ∧3) /2))) /
((((((¬(5 /¬(((7 ∨6) ∧¬7) /6)) /(((7 ∨6) ∧¬7) /6)) ∧¬(5 /¬(((7 ∨6) ∧¬7) /6))) /
(((7 ∨6) ∧¬7) /6)) /4) ∧(((¬(5 /¬(((7 ∨6) ∧¬7) /6)) /(((7 ∨6) ∧¬7) /6)) ∧¬(5 /
¬(((7 ∨6) ∧¬7) /6))) /(((7 ∨6) ∧¬7) /6))) /4))
The numbers refer to the unit identifiers used in the RST analysis and within its
respective relational proposition. Just as the RST structure identifies unit 4 as the
locus of intended effect, its logical counterpart implies unit 4.
The fourth step, leveraging the principle of transitivity, may now be taken.
Transitivity is a property of logical expressions through which Boolean values
propagate from an initial set of premises through an inferential path. In classical
logic, the principle of transitivity is exemplified in the pure hypothetical syllogism:
6Potter
(((p /q) ∧(q /r)) /(p /r))
Transitivity provides the means for logical compression. In the case of hypothetical
syllogism ((p /q) ∧(q /r)) can be compressed to (p /r). Although canonical
instances of hypothetical syllogism are unusual in discourse, other transitive
structures are common. Transitivity permits squeezing out intermediary inferences
Table :Summary of RST logical definitions.
Relation/predicate Logical form
ANTITHESIS (((s ∨n) ∧¬s) →n)
Disjunctive syllogism. The intended effect is to increase the reader’s
positive regard for the nucleus. The satellite and nucleus are incom-
patible, hence the reader cannot have positive regard for both. This
incompatibility increases the reader’s positive regard for the nucleus.
CONCESSION (((¬(s →¬n) →n) ∧¬(s →¬n)) →n)
Modus ponens. The writer concedes the situation presented in the
satellite and asserts that, though there might seem to be a potential
incompatibility between the satellite and the nucleus, the satellite and
nucleus are indeed compatible. The writer holds the nucleus in positive
regard, and by indicating a lack of incompatibility with the satellite, the
writer seeks to increase the reader’s positive regard for the nucleus.
BACKGROUND
CAUSE
CIRCUMSTANCE
ELABORATION
ENABLEMENT
EVIDENCE
JUSTIFY
MOTIVATION
PREPARATION
RESULT
SOLUTIONHOOD
(((s →n) ∧s) →n)
Modus ponens. Each relation, within a specified Boolean domain, uses
the satellite to realize an effect. For example in EVIDENCE, the satellite
provides evidence in support of the nucleus. For the relation to achieve
its intended effect, it is necessary that the reader accept the satellite.
In ELABORATION, the satellite illuminates and lends clarity to the nucleus,
thereby imparting greater understanding. MOTIVATION increases the
reader’s desire to perform the action, and ENABLEMENT informs the reader
how to do so. BACKGROUND is used to assure comprehensibility of the
text, and PREPARATION is used to gain interest.
EVALUATION
INTERPRETATION
(((n →s) ∧s) →s)
Modus ponens. EVALUATION and INTERPRETATION involve assessment of the
situation presented in the nucleus. EVALUATION assesses the situation
presented by the nucleus with respect to the writer’s positive regard.
INTERPRETATION relates the nuclear situation to a framework of ideas not
involved in the nucleus and not concerned with the writer’s positive
regard.
CONDITION
PURPOSE
(s →n)
Implication. In some cases CONDITION will be biconditional.
CONJUNCTION
JOINT
(n∧n)
Logical conjunction.
Text as tautology 7
and arguments. For complex logical expressions, it is possible and convenient to
use relational propositions as surrogates for logical expressions, thus simplifying
presentation and analysis. The procedure for this is subject to some constraints.
A detailed example is provided in Section 4.2.
The fifth and final step is to circle back and apply the compression to the text
and assess the result. For the texts included in this study, the application of
transitive inference to the logical expressions usually results in abridged texts that
are intuitively coherent and logical consequents of their originals. When this fails
to happen, it will be shown, the problem arises due to a discrepancy in the RST
analysis. And this in turn suggests that the methodology used here can serve,
among other things, as a means for RST validation.
4 Analysis
In this section the analytical procedure is applied to the RST analyses identified in
Section 2, with an accompanying commentary. This includes stepwise analyses
showing how transitivity enables compression, and shows how relational propo-
sitions can be used as logical surrogates, thus simplifying the procedure. Included
in the analysis is a detailed explanation of the handling of defeasibility as intro-
duced in Section 2. This is followed by analyses of several special cases, including
non-tautological relations, multinuclear relations, and conjunctive satellites.
Finally, I show how the procedure can be used to support RST validation.
4.1 Transitivity of relational propositions
In defining a thread of discourse, transitivities render the essence of logical integrity.
The first example to be considered is the Leading Indicators analysis, shown in
Figure 2.
The logic ranges over multiple Boolean domains. The relational proposition is
preparation(1,interpretation(concession(5,6),elaboration(evidence(4,3),2)))
The assessment provided in unit 6follows from the inferential path specified in
units 1–5.
((1 /((((((4 /3) ∧4) /2) ∧((4 /3) ∧4)) /((¬(5 /¬6) /6) ∧¬(5 /¬6))) ∧((((4 /3)
∧4) /2) ∧((4 /3) ∧4)))) ∧1)
From the expression above, it follows transitively that (1 /6). The inferred rela-
tional proposition is preparation (1,6), such that the title segment, Leading Indicators
8Potter
provides the reader with context for the observation that …the current protracted
sluggishness of leading indicators appears consistent with our prognosis…Key to
realizing this as an inference is the multiplicity of Boolean domains. Implicit in
relational propositions is a logic that is complex not only in its inference structure
but in the scope of its intentionalities. While the exercise of logic as traditionally
conceptualized is delimited, a uniform Boolean domain (typically true and false),the
logic of reasoning, as manifest in discourse, is subject to no such restriction. It
operates seamlessly across a range of intentionalities, such as belief and disbelief,
action and inaction,acceptance and rejection,andcomprehension and incompre-
hension, traversing from one inference to the next, as the writer develops an intended
effect. As such, what might seem a peculiarity for logic is an ordinary feature in
discursive reasoning. The logic of relational propositions provides a framework for
subsuming these Boolean domains as a generalized Boolean data type.
While the coherence of the full text arises from a concatenation of inferential
intentionalities, transitivity licenses its reduction to inferential termini, subsuming
the discrete domains under the abstract data type of discursive coherence. When
transitivity is selectively applied, the process is one of stepwise compression,a
procedure for examining the tautological essence of discursive coherence. For any
transitive text, it is possible to reduce its logical expression not only to its infer-
ential termini, but to reduce it progressively, removing points between the initial
premise and the terminal inference. This suggests a stepwise procedure for elim-
inating selective intermediary relational propositions from within an inferential
path. This involves identification of the initial premise, terminal inference, and
inferential path. Within that path, we can eliminate the most deeply nested rela-
tional propositions. At each step of the compression, the compressed logical
Figure 2: Leading Indicators RST analysis (Mann et al. 2000).
Text as tautology 9
expression follows transitively from its predecessor. The first step is to eliminate
evidence(4,3) from the expression:
((1 /((((((4 /3) ∧4) /2) ∧((4 /3) ∧4)) /((¬(5 /¬6) /6) ∧¬(5 /¬6))) ∧((((4 /3)
∧4) /2) ∧((4 /3) ∧4)))) ∧1)
This yields the compression,
((1 /((((3 /2) ∧3) /((¬(5 /¬6) /6) ∧¬(5 /¬6))) ∧((3 /2) ∧3))) ∧1)
From this compressed expression, we can then remove elaboration (3,2):
((1 /((2 /((¬(5 /¬6) /6) ∧¬(5 /¬6))) ∧2)) ∧1)
Following this, concession(5,6) may be eliminated. Its elimination results in the
following:
((1 /((2 /6) ∧2)) ∧1)
And finally in removing interpretation (2,6), note that the inferential path for
INTERPRETATION is nucleus /satellite. Both INTERPRETATION and EVALUATION involve
assessment of the situation presented in the nucleus. What remains is the logic for
the preparation predicate:
((1 /6) ∧1) /6
This corresponds to preparation(1,6). The compressions are licensed by the logic. Yet
there is nothing particularly remarkable about it. What is significant is that since the
expressions serve as models of discourse coherence, the operations permissible on
the models preserve coherence when applied to the text. The transitivity of nested
relational propositions indicates logical license to do so.Discursively, segments are
dropped from the text, leaving readers with an abbreviated version. However, the
discursive coherence survives, as illustrated in Figure 3, indicative of the logical
essence of discursive integrity.
It might appear that the complexities of transitivity are unnecessary, that we
would accomplish the same thing simply by pruning the leaves from the RST tree.
However, this is not the case. Not only does transitivity provide license for elimi-
nation of select relational propositions, it prescribes what may be eliminated, and
what may not. Only expressions constituting tautologies, i.e. valid arguments, may
be compressed. Other expressions, such as conditionals, conjunctions, disjunc-
tions, and multinuclear relations may be eliminated only when they are positioned
as eliminable premises. Moreover, among tautologous relations, it is not uniformly
the case that the inferential path flows from satellite to nucleus, but rather for some
relations inference flows from nucleus to satellite.
10 Potter
Figure 3: Stepwise compression of the Leading Indicators RST analysis.
Text as tautology 11
4.2 Relational propositions as logical surrogates
Subject to the abovementioned constraints, however, it is possible and convenient
to use relational propositions as surrogates for logical expressions, thus simpli-
fying presentation and analysis. This allows us to focus on the compression at a
higher level of conceptualization. Below is the stepwise compression for the Not
Laziness analysis:
background(result(1,circumstance(3,2)),evidence(concession(5,antithesis(7,6)),4))
background(result(1,circumstance(3,2)),evidence(concession(5,6),4))
background(result(1,circumstance(3,2)),evidence(6,4))
background(result(1,2),evidence(6,4))
background(2,evidence(6,4))
background(2,4)
Applying these to the text results in a series of progressively succinct renderings
with he final step capturing the essence of the text:
Hundreds of people lined up to be among the first applying for jobs at the yet-to-open Marriott
Hotel. The people waiting in line carried a message, a refutation, of claims that the jobless could
be employed if only they showed enough moxie.
In another example, in the RST analysis shown in Figure 4, EVALUATION is used to
assess the situation described in segments 1–3. The inferential path of EVALUATION,
as with INTERPRETATION,flows from the nucleus to the satellite. That this is the correct
logical form for the relation is manifest in the application of stepwise compression
to the RST analysis. The relational proposition is
evaluation(antithesis(condition(4,5),6),elaboration(3,antithesis(1,2)))
The inferential path shows the logic flowing from segments 3 to 6:
((((((3 /(((1 ∨2) ∧¬1) /2)) ∧3) /(((1 ∨2) ∧¬1) /2)) /((((4 /5) ∨6) ∧¬(4 /5)) /
6)) ∧(((3 /(((1 ∨2) ∧¬1) /2)) ∧3) /(((1 ∨2) ∧¬1) /2))) /((((4 /5) ∨6) ∧¬(4 /5))
/6))
As can be seen below, the stepwise compression confirms this:
evaluation(antithesis(condition(4,5),6),elaboration(3,antithesis(1,2)))
12 Potter
evaluation(antithesis(condition(4,5),6),elaboration(3, 2))
evaluation(6,elaboration(3, 2))
evaluation(6, 2)
This results in the following summary:
International agencies and foreign powers should put their effort into the more ambitious project
of building a functional Haitian state …To patch up a dying country and call it a rescue would
leave Haiti forsaken indeed, and not by God.
4.3 Intentional defeasibility
An important, if obvious, characteristic of discursive reasoning is that it occurs
within a discourse. The text presents a perspective that delimits the reasoning to
the writer’s universe of discourse. The writer uses relational propositions to
anticipate the effect of the discourse on the reader. If an inference is intended as
defeasible, it is the writer’s job to indicate it as such. That is, the defeasibility is
built into the discourse. The reader is at liberty to regard as defeasible what the
writer has intended as unassailable. This occurs when the reader disagrees with
the writer. When the reader interacts with the discursive reasoning in a way
unanticipated by the writer, the universe of discourse is effectively extended
beyond the text, at which point the reasoning becomes extratextual. But this is not
to say that the discourse becomes defeasible. When the reasoning becomes
Figure 4: The New Yorker RST analysis excerpt (Stede et al. 2017).
Text as tautology 13
extratextual, the analysis is no longer just about the text, but about the reader’s
unanticipated interaction with the text. The logic of relational propositions seeks
to represent the unextended universe of discourse, that is to say, the logic of the
writer’s intended effect.
So what I am trying to examine here is not the reader’s reaction, but the writer’s
intentions, what the writer wants the reader’s reaction to be. When defeasibility is
intended, it would behoove the writer to so indicate. The defeasibility will be built-
in. In the RST Analysis shown in Figure 5, the view that dioxin is harmless is
presented as less than certain. The supporting satellite, coded as an ELABORATION
(and could have been EVIDENCE) is insufficient to assure certitude of the harmless-
ness of the chemical. Indeed, a lack of evidence of long-term effects falls short of
assuring that there would be no ill effects, and as subsequent research has
demonstrated, dioxin is toxic for animals and humans alike. Thus the argument is
positioned as defeasible, but since the defeasibility is internalized the logical
structure is deductive, as with any other inferential relational proposition.
4.4 Non-tautological relations
Non-tautological relations include multinuclear relations and conditional or un-
realized relations, such as CONDITION and PURPOSE. These relations cannot be logi-
cally compressed. Except for DISJUNCTION, multinuclear relations are conjunctive.
CONDITION and PURPOSE are implicative but not inferential. When they occur as sat-
ellites to an inferential relation they may be eliminated, but as nuclei, unless the
relational proposition is positioned as part of a larger eliminable expression, they
must remain intact in the compressed expression.
Figure 5: Dioxin RST analysis (Mann and Thompson 1988).
14 Potter
4.5 Eliminable non-tautological relations
In Frege’s argument against psychologism, shown in Figure 6, the CONDITION rela-
tion can be eliminated because it is the satellite to a CONCESSION relation.
The stepwise compression consists of just two steps:
evidence(concession(condition(2,3),4),1)
evidence(4,1)
What remains of the argument (Figure 7) is the analogy between arithmetic
andastronomy,andthedenialofthecomparability to psychology, thereby
providing evidence against the claim that number is the idea of the position of an item
in a series.
Figure 6: Frege’s argument against psychologism RST analysis (Potter 2020).
Figure 7: Frege’s argument against psychologism RST analysis fully compressed.
Text as tautology 15
4.5.1 Non-eliminable non-tautological relations
An example of a non-tautological relation that cannot be eliminated can be found
in the Bouquet analysis, shown in Figure 8.
The stepwise compression is as follows:
background(elaboration(elaboration(3,2),1),
purpose(4,conjunction(elaboration(6,5),elaboration(elaboration(8,7),5)))
background(elaboration(elaboration(3,2),1),purpose(4,conjunction(elaboration(6,5),
elaboration(7,5)))
background(elaboration(elaboration(3,2),1),purpose(4,conjunction(5, 5)))
background(elaboration(elaboration(3,2),1),purpose(4,5))
background(elaboration(2,1),purpose(4,5))
background(1,purpose(4,5))
PURPOSE as nucleus cannot be logically compressed, so it is preserved in the
compression, as shown above in Figure 9.
Figure 8: Bouquets in a Basket RST analysis (Mann and Thompson 1987a).
Figure 9: Bouquets in a Basket RST
Analysis, fully compressed.
16 Potter
4.6 Multinuclear relations
The CONJUNCTION,CONTRAST,JOINT,LIST,andMULTI NUCLEAR RESTATEMENT relations are
logically conjunctive. When occurring as nuclei of inferential relations they may
be simplified using conjunction elimination, but not compressed. When occur-
ring as satellite, they can be neither compressed nor simplified without making
assumptions about the realization of intended effect. Figure 10 shows an ELABO-
RATION relation containing multinuclear relations in both the satellite and nuclear
positions.
The possibility for compression is limited, as can be seen here:
elaboration(contrast(12,13),restatementmn(circumstance(9,10),11))
elaboration(contrast(12,13),restatementmn(10,11))
Given the redundancy of RESTATEMENT relations, eliminating one of the conjuncts
might be acceptable, but in this particular case, that action appears only to suggest
the possibility that it is not actually a restatement, but perhaps an EVALUATION.
Not all multinuclear relations are conjunctive. The DISJUNCTION relation is, as the
name suggests, logically disjunctive, either exclusively or inclusively. In neither
form is it compressible, since the disjuncts cannot be individually inferred. The
SEQUENCE relation is more interesting. Figure 11 shows an example of a sequence
based on a recipe.
The logical form for this relation is ((((5 ↔4) ↔3) ↔2) ↔1). It specifies an
order-dependent set and is therefore not compressible. Note that sequences need
Figure 10: ZPG RST analysis excerpt (renumbered).
Text as tautology 17
not be multinuclear. When the relation between members of the series is iden-
tifiable, e.g. causal sequences, satellite-nuclear relations may be applicable, and
the approach to compression would follow the practice defined for inferential
relations.
4.7 Conjunctive satellites
A nucleus may be the locus of multiple intended effects, such that multiple sat-
ellites converge conjunctively in support of a shared nucleus. Consider the Syncom
analysis shown in Figure 12.
The RST analysis contains two occurrences of conjunctive satellite conver-
gence. The first of these is in text span 3–12. Here, four ELABORATION satellites
converge on the 3–5 text span. Each ELABORATION identifies one of the four ways the
Syncom diskette works to keep loose particles and dust from causing errors. The
circumstance(3, purpose(5,4)) proposition is the nucleus of the conjunction of four
elaboration satellites. The conjuncts are as follows:
elaboration(circumstance(7,6),circumstance(3,purpose(5,4)))
elaboration(antithesis(8,9),circumstance(3,purpose(5,4))))
elaboration(10, circumstance(3,purpose(5,4))))
elaboration(antithesis(12,11), circumstance(3,purpose(5,4))))
Compressing these conjuncts simplifies the expression, making it easier to
analyze. However, before proceeding to the compression it is necessary to make a
correction to antithesis(8,9). Assigning 10 as the nucleus has the effect of indi-
cating that before it can attract dust or lint is one of the four ways that the Syncom
diskette protects the floppy drive, when clearly it is the carbon additive draining
away static electricity that performs this function. A more likely relation would be
circumstance(9,8). With this correction, the compressions of the four elaboration
satellites are
Figure 11: Orange Magnolia Recipe RST analysis (Mann and Thompson 1987b).
18 Potter
Figure 12: Syncom RST analysis (Mann and Thompson 1987b).
Text as tautology 19
elaboration(6,circumstance(3,purpose(5,4)))
elaboration(6,purpose(5,4))
elaboration(8,circumstance(3,purpose(5,4)))
elaboration(8,purpose(5,4))
elaboration(10,circumstance(3,purpose(5,4)))
elaboration(10,purpose(5,4))
elaboration(antithesis(12,11),circumstance(3,purpose(5,4)))
elaboration(11,purpose(5,4))
This results in the following conjunction:
conjunction(
elaboration(6,purpose(5,4)),
elaboration(8,purpose(5,4)),
elaboration(10,purpose(5,4)),
elaboration(11,purpose(5,4)))
There is no further compression possible for this part of the text. purpose cannot be
compressed because it is unrealized, and conjuncts cannot be eliminated due to
their collective inferential relation to purpose(5,4).
The second set of conjunctive satellites is in the MOTIVATION-ENABLEMENT struc-
ture that encompasses text span 2–15. The MOTIVATION branch compresses as just
discussed. The ENABLEMENT branch of the analysis is simpler, and may be com-
pressed as follows:
enablement(purpose(13,enablement(15,14)),2)
enablement(purpose(13,14),2)
Taken together with the MOTIVATION, this provides both parts of the conjunctive
satellite. The corresponding RST diagram is shown in Figure 13.
This shows that conjunctive satellites must be treated as just that, conjunc-
tions of satellites. The compressed structure remains rather verbose. There is no
problem with this as far as transitivity is concerned. However, if we assume the
20 Potter
Figure 13: Syncom RST analysis compressed.
Text as tautology 21
effect of the conjoined elaboration propositions to be realized, permitting inference
of their nuclei, then the elaboration propositions can be eliminated entirely.
Often conjunctive satellites use a satellite-nucleus-satellite schema, in which
the satellites flank both sides of the nucleus. Because relational propositions are
order independent this makes no difference for the compression. The satellites are
conjunctive and the possibilities for compression are limited accordingly. In text
span 1–5 of Figure 14, this is further limited by the use of the multinuclear Joint
relation in one of the satellites:
justify(conjunction(justify(joint(1,2),3), justify(interpretation(5,4),3)),6)
justify(conjunction(justify(joint(1,2),3), justify(4,3)),6)
Again, the issue of verbosity is encountered. The same technique applied above to
the Syncom analysis can be applied here:
justify(conjunction(justify(joint(1,2),3), justify(interpretation(5,4),3)),6)
justify(conjunction(3,3),6)
justify(3,6)
For the MOTIVATION-ENABLEMENT schema the case for use of conjunctive satellites
seems sound. The relations combine to produce an accrued intended effect.
However, if the transitivity of relations is a consideration of value, as is argued in
this paper, then use of conjunctive satellites should be conservative. It would be
appropriate for analysts to tease out hierarchy wherever it can be found, not merely
because it might support the agenda discussed in this paper (which it would), but
because it would result in more interesting, nuanced analyses.
In the example in Figure 15, the BACKGROUND and MOTIVATION satellites attach to
the same nucleus. The satellites converge conjunctively in support of a shared
nucleus. The relational proposition for this RST analysis is as follows:
motivation(conjunction(background(1,2),motivation(3,2),motivation(4,2)),5)
Using the techniques described above, this can be reduced to motivation(2,5),shown
in Figure 16. Discursively, this is a bit weak: Being careful in the wilderness may be
sound advice, but without the context providedby the satellites, it may be difficult to
make the connection between being careful and locating meat and deciding what
clothing to sleep in. Conjunctive satellites are logically flat yet information-rich, so
their elimination can result in strained coherence. A more hierarchical interpretation
yielding slight differences in span organization significantly alters the logical
22 Potter
Figure 14: World Wildlife Fund RST analysis last paragraph (Abelen et al. 1993).
Text as tautology 23
interpretation. Suppose the analyst had designated the nucleus of background as
text span 2–4 rather than unit 2 (see Figure 17):
motivation(background(1,conjunction(motivation(3,2),motivation(4,2))),5)
Figure 16: Bears in Ontario RST analysis
compression.
Figure 15: Bears in Ontario RST analysis (Stede et al. 2017).
Figure 17: Bears in Ontario modified compression.
24 Potter
This would support the transitivity as follows:
motivation(background(1,2),5)
The above yields a more informative relational proposition. This suggests that
inferentially dense RST analyses are more conducive to richer interpretations than
conjunctive satellites, and it supports Potter’s (2018) claim that problematic logical
analyses are indicative of questionable RST analyses. This raises the possibility
that stepwise compression may be useful for RST validation.
4.8 RST validation
Stepwise compression sometimes leads to counterintuitive results. This indicates a
problematic analysis, as was encountered above with the Syncom analysis, where
the nuclearity was reversed and an incorrect relation was assigned. A similar
example is shown in Figure 18.
Of particular interest are segments 1–3, for which the relational proposition is:
solutionhood(concession(3,2),1)
The transitive compression of this is:
solutionhood(2,1)
For this relation to hold, the satellite (2) must be a problem to which the nucleus (1)is
a solution. That would be to say, senate membership among retired faculty is a
Figure 18: Emeriti Committee RST
analysis (Thompson and Mann
1987).
Text as tautology 25
problem for which establishment of a committee is the solution. But this is does not
readily follow. That retired faculty members remain members of the Senate is not the
problem. The problem is that retired faculty lack representation despite their mem-
bership. The difficulty with the RST analysis is that the nuclearity of the CONCESSION
relation has been reversed. In a short and simple text like this it is fairly easy to spot
the difficulty, but not easy enough to prevent its occurrence. Compression offers an
alternative perspective, underscoring the problematic relation. An emended RST
analysisisshowninFigure19.
The relational proposition may now be compressed as follows:
solutionhood(concession(2,3),1)
solutionhood(3,1)
This compression correctly positions segment 3 as the problem to which 1 is the
solution, and as the implicatum of the CONCESSION. The takeaway message is not that
some RST analyses contain errors—these are common enough—but that the associ-
ation of logical transitivity with rhetorical structure is sufficiently robust that dis-
crepancies in analysis tend to propagate and manifest through the inferential path.
Another example can be found in the RST diagram shown in Figure 20,
excerpted from Mann and Thompson’s CCC analysis.
The compression for this argument is as follows:
concession(11,antithesis (12,13))
concession(11,13)
Figure 19: Emended Emeriti
Committee RST analysis.
26 Potter
The resulting compression then is:
I personally favor the initiative and ardently support disarmament negotiations to reduce the
risk of war. We should limit our involvement in defense weaponry to matters of process, such as
exposing the weapons industry’sinfluence on the political process.
The coherence of this, while not impossible, is difficult, with the second sentence
seeming at odds with the first. Returning to the RST analysis, the question again
arises as to what exactly is being conceded. Arguably, the CONCESSION relation
should be between 11 and 12 rather than 11 and 12–13. Diagrammatically, the
distinction is perhaps subtle (Figure 21), but the resulting refinement in the
inferential path is noticeable.
Figure 20: The Political Text (CCC)
RST analysis segments 10–13
(Mann and Thompson 1985).
Figure 21: The Political Text (CCC)
RST analysis 10–13 (Mann and
Thompson 1985).
Text as tautology 27
Here is the stepwise compression for the corrected version:
antithesis(concession(11,12),13)
antithesis(12,13)
So now the resulting compression reads as follows:
…I don’t think endorsing a specific nuclear freeze proposal is appropriate for CCC. We should
limit our involvement in defense weaponry to matters of process, such as exposing the weapons
industry’sinfluence on the political process.
The second sentence follows readily from the first and the two taken together
capture the essence of the argument. An RST analysis that cannot pass the test of
logic is an analysis in need of attention.
5 Conclusions
In this paper, the logic of relational propositions was used to explore the appli-
cability of transitive inference operations to written discourse. Using a set of RST
analyses taken from the literature, the method was used to identify their corre-
sponding logical expressions. For each expression, by eliminating intermediary
relational propositions from within the inference path, transitivity was used to
compress the expression. The resulting compressions were then applied to their
corresponding texts. RST was used to assess the coherence of the results. The
application of transitive inference to the logical expressions results in abridged
texts that are coherent and compatible with their originals. This indicates an un-
derlying isomorphism between the inferential structure of logical expressions and
the discursive coherence of the texts, such that these expressions function as
logical models of the text, and it shows that propositional logic is a significant
component of discursive coherence, thus enabling manipulation of discourse as
logical expressions. The application of compression to problematic RST analyses
revealed that the problems in the originals were highlighted in the compressions,
showing how compression can be used as an aid in evaluating RST analysis. The
distinctive contribution of this paper is then in the provision, not only for mappings
between discourse and rhetorical structure and between rhetorical structure and
logic, but with support for the claim that operations performed at the logical level
will have plausible discursive analogs.
28 Potter
This ability to render relational propositions as logical expressions suggests a
general method for mining discourse for occurrences of rules of inference, and
when combined with the properties of transitivity and compression, this could be
used to support automated reasoning processes, such as those used in the infer-
ence engines of knowledge-based systems. In particular, this could support
controlled natural languages, such as the Logical English system described by
Kowalski (2020) or the Attempto CNL system developed by Fuchs (2018). If inte-
grated with an automated RST parser (Hou et al. 2020), this opens the possibility of
generating knowledge bases from texts. Although the ability to automatically
generate RST analyses from texts has proven challenging, work continues (Hou et
al. 2020).
The technique may also be of value to students of logic and argumentation.
Textbooks in logic typically provide guidance for the application of logic to natural
language (e.g., Copi 1972; Hurley 2012). This guidance tends to be less than sys-
tematic and is restricted to truth functions, whereas the logic of relational prop-
ositions ranges over multiple Boolean domains. Since any RST analysis can be
restated as a relational proposition, and any relational proposition can be restated
as a logical expression, this provides an alternative route to translating natural
language arguments into propositional logic.
Identification of transitivity as a property of discourse coherence has direct
consequences for what has become known as the strong nuclearity hypothesis in
rhetorical structure theory (Das 2019; Stede 2008). This assumption postulates that
the nucleus of a composite branch structure will hold the same relation to the
parent as the composite branch itself. This assumption is implicit in Mann and
Thompson’s (1987b) discussion of nuclearity, it was made explicit in Marcu’s
(1996, 2000) development of RST summarization study, and it has been used in
discourse relation detection (Zeldes and Liu 2020), fake review detection (Popoola
2017), and in efforts to unify disparate coherence relations theories (Sanders et al.
2018). If transitivity holds, then the nucleus of a composite branch structure will
follow logically from its satellites, and thus strong nuclearity may be treated as an
observable property of discourse coherence. Thus the compression technique
described in this paper contributes to epistemic support for RST-based summari-
zation, relation detection, and rhetorical structure theory in general.
Research funding: Not applicable.
Availability of data and material: Not applicable.
Code availability: Not applicable.
Competing interests: Not applicable.
Text as tautology 29
Appendix: Source articles
–Not Laziness (Mann and Thompson 1988)
–Dioxin (Mann and Thompson 1988)
–Bears in Ontario (Stede et al. 2017)
–Bouquets in a Basket (Mann and Thompson 1987a)
–Emeriti Committee (Thompson and Mann 1987)
–Frege’s Argument Against Psychologism (Potter 2020)
–Haiti (Stede et al. 2017)
–Leading Indicators (Mann et al. 2000)
–Orange Magnolia Recipe (Mann and Thompson 1987b)
–Syncom Analysis (Mann and Thompson 1988)
–The Political Text (CCC) (Mann and Thompson 1985)
–World Wildlife Fund (Abelen et al. 1993)
–ZPG Analysis (Mann and Thompson 1992; Toulmin 1958)
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Bionote
Andrew Potter
Department of Computer Science & Information Systems, University of North Alabama, Florence,
AL, USA
apotter1@una.edu
https://orcid.org/0000-0001-8866-4714
32 Potter
Andrew Potter received his PhD in Information Science from Nova Southeastern University and is
currently an Assistant Professor at the University of North Alabama. His research interests include
the intersection of Rhetorical Structure Theory, Relational Propositions, Logic, and Knowledge
Representation. His most recent publication is The rhetorical structure of modus tollens: An
exploration in logic-mining, which can be found in the Proceedings of the Society for Computation
in Linguistics for the year 2020.
Text as tautology 33
