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Logic and Ontology
Abstract
A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue that anextended form of conceptual realism provides themost coherent formal ontology and, as such, canbe used to defend the view of logic as language.
... Given this necessary historical background, let us now illustrate shortly a taxonomy of the main formal ontologies proposed in the history of Western thought. This synthesis is inspired by a similar one developed by my colleague and friend Nino B. Cocchiarella [60,61], a logician and philosopher of logic, now Emeritus at the Philosophy Dept. of the Indiana University at Bloomington (USA). What I share with him-apart from some significant differences-is the general idea that the main ontologies of whichever philosophy and culture can be interpreted, in formal philosophy, like many theories of predication, as far as predication is not reducible to the only class/set membership relation ∈. ...
... To sum up [60][61][62], we can synchronically distinguish along the centuries of the (Western) history of thought (generally distinct into Ancient, Middle, and Modern Ages) at least three types of ontologies, with the last one subdivided into two others (see Figure 2). For each of these subdivisions, I quote indicatively in parenthesis some authors, who belong indifferently to one of the three main ages of the Western tradition 8 . ...
... This depends on the socalled "ultrafilter lemma" for which any proper filter is the intersection of all ultrafilters containing it, requiring that free ultrafilters for existence must be defined on infinite sets (see [149], pp. [57][58][59][60][61][62][63][64][65][66][67][68]. Therefore, the ultrafilters lemma supposes in ZF the "axiom of choice" (hence ZFC), or the "Zorn's lemma", as was the case of Stone's demonstration of RTBA. ...
This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences.
... une ontologie) basée sur le bon sens et la découverte plutôt qu'inventée, la spécication de la sémantique devenait alors triviale. Par ailleurs, dans [33] Cocchiarella proposa d'identier la logique à un langage, contrastant ainsi avec la vision classique qui la voit comme un calcul. La logique possède alors un contenu ontologique, et pour cela l'auteur indique qu'il est nécessaire d'utiliser une théorie des types, plutôt que la théorie des ensembles, comme cadre de travail. ...
... Elle dénit également un niveau ontologique qui permet de donner une signication propre à des notions telles que des propositions, la vérité de ces propositions, les relations de conséquences entre les propositions et des relations complexes. Pour nir, un niveau logique est déni interagissant avec les deux précédants niveaux au sens de Cochiarella [33]. Ce niveau fournit un langage susamment riche et expressif pour le raisonnement sur des connaissances et sur les structures formelles valides décrivant des parties de situations. ...
This approach suggests a possible solution for the following issue : how to formalize environments related to a given process and how to exploit the information they provide in order to start appropriate actions ? For that purpose, we took an interest in the concepts of ontologies, contexts and actions. We have investigated the constructive type theory and extended it with extensional sub-typing (allowing for type hierarchies) and constants to result in what is called the Dependent Type Framework (DTF). DTF tries to combine a constructive logic with a functional programming language for the representation and reasoning about contexts and actions. It provides a high expressiveness, decidability of type checking and a powerful sub-typing mechanism. We show how to model both contexts with types in DTF from the given information about a problem and actions to start to solve it. Then, as a test of feasibility with the purpose of sensing the complexity of such a solution, a context prover has been built with a functional language. Finally, a test application called the wumpus world in which a software agent moves across a grid in an unknown environment is implemented.
... First, we believe that a commonsense theory of the world can (and should) be embedded in our semantic formalisms resulting in a logical semantics grounded in commonsense metaphysics. Moreover, we believe the first step to accomplishing this vision is rectifying what we think was a crucial oversight in logical semantics, namely the failure to distinguish between two fundamentally different types of concepts: (i) ontological concepts, that correspond to what Cocchiarella (2001) calls firstintension concepts and are types in a strongly-typed ontology; and (ii) logical concepts (or second intension concepts), that are predicates corresponding to properties of (and relations between) objects of various ontological types 1 . ...
In the concluding remarks of Ontological Promiscuity Hobbs (1985) made what we believe to be a very insightful observation: given that semantics is an attempt at specifying the relation between language and the world, if "one can assume a theory of the world that is isomorphic to the way we talk about it ... then semantics becomes nearly trivial". But how exactly can we rectify our logical formalisms so that semantics, an endeavor that has occupied the most penetrating minds for over two centuries, can become (nearly) trivial, and what exactly does it mean to assume a theory of the world in our semantics? In this paper we hope to provide answers for both questions. First, we believe that a commonsense theory of the world can (and should) be embedded in our semantic formalisms resulting in a logical semantics grounded in commonsense metaphysics. Moreover, we believe the first step to accomplishing this vision is rectifying what we think was a crucial oversight in logical semantics, namely the failure to distinguish between two fundamentally different types of concepts: (i) ontological concepts, that correspond to what Cocchiarella (2001) calls first-intension concepts and are types in a strongly-typed ontology; and (ii) logical concepts (or second intension concepts), that are predicates corresponding to properties of (and relations between) objects of various ontological types1. In such a framework, which we will refer to henceforth by ontologik, it will be shown how type unification and other type operations can be used to account for the `missing text phenomenon' (MTP) (see Saba, 2019a) that is at the heart of most challenges in the semantics of natural language, by uncovering the significant amount of missing text that is never explicitly stated in everyday discourse, but is often implicitly assumed as shared background knowledge.
... 3 Cf. (Cocchiarella, 2001) for a discussion of logic as language (primacy of the predicative function) vs logic as calculus (primacy of set theory) in questions of ontology. ...
... Thus, and although Beautif ul applies to objects of type Entity, in saying 'a beautiful car' , for example, the meaning of Beautif ul that is accessed is that defined in the type Physical(which could in principal be inherited from a supertype). Moreover, and as is well known in the theory of programming languages, one can always perform type casting upwards, but not downwards (e.g., one can always view a Car as just an Entity, but the converse is not true) 3 . Thus, assuming Red(x :: Physical) and Beautif ul(x :: Entity); that is, assuming that 'red' can be said of Physical objects and 'beautiful' can be said of any Entity, and using the notation A1(A2(x :: t2) :: t1) to represent adjectives A1 and A2 that are assumed to apply to objects of type t1 and t2, respectively, then, for example, the type casting that will be required in (11a) is valid, while that in (11b) is not This, in fact, is precisely why 'Jon owns a beautiful red car' is more natural than 'Jon owns a red beautiful car' . ...
We suggest modeling concepts as types in a strongly-typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. In such a framework, certain types of ambiguities in natural language are explained by the notion of polymorphism. In this paper we suggest such a typed compositional semantics for nominal compounds of the form (Adj Noun) where adjectives are modeled as higher-order polymorphic functions. In addition to (Adj Noun) compounds our proposal seems also to suggest a plausible explanation for well known adjective ordering restrictions.
... The point of this informal explanation is to suggest that the problem underlying most challenges in the semantics of natural language seems to lie in semantic formalisms that employ logics that are mere abstract symbol manipulation systems; systems that are devoid of any ontological content. What we suggest, instead, is a compositional semantics that is grounded in commonsense metaphysics, a semantics that views " logic as a language " ; that is, a logic that has content, and ontological content, in particular, as has been recently and quite convincingly advocated by Cocchiarella (2001). In these working notes we propose exactly such an approach. ...
In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link with our common-sense view of the world, and it is quite difficult to envision how one can formally account for the considerable amount of content that is often implicit, but almost never explicitly stated in our everyday discourse. The solution, in our opinion, is a compositional semantics grounded in an ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. In the compositional logic we envision there are ontological (or first-intension) concepts, and logical (or second-intension) concepts, and where the ontological concepts include not only Davidsonian events, but other abstract objects as well (e.g., states, processes, properties, activities, attributes, etc.) It will be demonstrated here that in such a framework, a number of challenges in the semantics of natural language (e.g., metonymy, intensionality, metaphor, etc.) can be properly and uniformly addressed.
... sheba is a young artist In the final analysis, therefore, 'sheba is a young artist' is interpreted as follows: there is a unique object named sheba, an object of type human, and such that sheba is Artist and Young 2 . Note here that in contrast with human, which is a first-intension ontological concept (Cocchiarella, 2001), Artist and 2 The type unifications in (4) can occur in any order since (r • (s • t)) = ((r • s) • t). That is, type unification is associative (and of course commutative), and this is a consequence of the fact that (r (s t)) = ((r s) t), where is the least upper bound (lub) operator. ...
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language phenomena may become nearly trivial.
... Thus, and although Beautif ul applies to objects of type Entity, in saying 'a beautiful car' , for example, the meaning of Beautif ul that is accessed is that defined in the type Physical(which could in principal be inherited from a supertype). Moreover, and as is well known in the theory of programming languages, one can always perform type casting upwards, but not downwards (e.g., one can always view a Car as just an Entity, but the converse is not true) 3 . Thus, assuming Red(x :: Physical) and Beautif ul(x :: Entity); that is, assuming that 'red' can be said of Physical objects and 'beautiful' can be said of any Entity, and using the notation A1(A2(x :: t2) :: t1) to represent adjectives A1 and A2 that are assumed to apply to objects of type t1 and t2, respectively, then, for example, the type casting that will be required in (11a) is valid, while that in (11b) is not This, in fact, is precisely why 'Jon owns a beautiful red car' is more natural than 'Jon owns a red beautiful car' . ...
We suggest modeling concepts as types in a strongly-typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. In such a framework, certain types of ambiguities in
natural language are explained by the notion of polymorphism. In this paper we suggest such a typed compositional semantics for nominal compounds of the form (Adj Noun) where adjectives are modeled as higher-order polymorphic functions. In addition to (Adj Noun) compounds our proposal seems also to suggest a plausible explanation for well known adjective ordering restrictions.
... Thus, and although Beautif ul applies to objects of type Entity, in saying 'a beautiful car' , for example, the meaning of Beautif ul that is accessed is that defined in the type Physical(which could in principal be inherited from a supertype). Moreover, and as is well known in the theory of programming languages, one can always perform type casting upwards, but not downwards (e.g., one can always view a Car as just an Entity, but the converse is not true) 3 . Thus, assuming Red(x :: Physical) and Beautif ul(x :: Entity); that is, assuming that 'red' can be said of Physical objects and 'beautiful' can be said of any Entity, and using the notation A1(A2(x :: t2) :: t1) to represent adjectives A1 and A2 that are assumed to apply to objects of type t1 and t2, respectively, then, for example, the type casting that will be required in (11a) is valid, while that in (11b) is not This, in fact, is precisely why 'Jon owns a beautiful red car' is more natural than 'Jon owns a red beautiful car' . ...
We suggest modeling concepts as types in a strongly-typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. In such a framework, certain types of ambiguities in natural language are explained by the notion of polymorphism. In this paper we suggest such a typed compositional semantics for nominal compounds of the form [Adj Noun] where adjectives are modeled as higher-order polymorphic functions. In addition to [Adj Noun] compounds our proposal seems also to suggest a plausible explanation for well known adjective ordering restrictions.
... It should be noted here that not recognizing the ontological difference between human and Artist (namely, that what ontologically exist are objects of type human, and not artists, and that Artist is a mere property that may or may not apply to objects of type human) has traditionally led to ontologies rampant with multiple inheritance. Note, further, that in contrast with human, which is a firstintension ontological concept (see [3] for a formal discussion on this issue), Artist and Young are considered to be second-intension logical concepts, namely properties that may or may not be true of first-intension (ontological) concepts. Moreover, and unlike first-intension ontological concepts (such as human), logical concepts such as Artist are assumed to be defined by virtue of logical expressions, such as ...
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. Assuming the existence of such a structure, we show that the semantics of various natural language phenomena may become nearly trivial.
... The point of this informal explanation is to suggest that the problem underlying most challenges in the semantics of natural language seems to lie in semantic formalisms that employ logics that are mere abstract symbol manipulation systems; systems that are devoid of any ontological content. What we suggest, instead, is a compositional semantics that is grounded in commonsense metaphysics, a semantics that views "logic as a language"; that is, a logic that has content, and ontological content, in particular, as has been recently and quite convincingly advocated by Cocchiarella (2001). ...
Over two decades ago a "quite revolution" overwhelmingly replaced knowledgebased approaches in natural language processing (NLP) by quantitative (e.g., statistical, corpus-based, machine learning) methods. Although it is our firm belief that purely quantitative approaches cannot be the only paradigm for NLP, dissatisfaction with purely engineering approaches to the construction of large knowledge bases for NLP are somewhat justified. In this paper we hope to demonstrate that both trends are partly misguided and that the time has come to enrich logical semantics with an ontological structure that reflects our commonsense view of the world and the way we talk about in ordinary language. In this paper it will be demonstrated that assuming such an ontological structure a number of challenges in the semantics of natural language (e.g., metonymy, intensionality, copredication, nominal compounds, etc.) can be properly and uniformly addressed.
If the project of formal ontology was first formulated by Edmund Husserl in his third Logical Investigation, it has been pursued during the last 40 years in the analytical tradition. In this paper, it is argued that formal ontology has been understood in at least two different ways in the analytic tradition. The first approach emphasizes its formal component and conceives formal ontology as a kind of formalised science of being. The second approach, which is more promising and closer to Husserl’s original project, claims that the formal domain contains a logical part and an ontological part, and that the two should not be confused. Therefore, according to this “substantial view” of formal ontology, there are formal structures that are properly ontological. In this paper, the two analytical approaches of formal ontology in contemporary analytic metaphysics are set out and it is shown that only the substantial view can really be considered as a theory of the object or something in general.
Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called ``substitutional". In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the nominalist's reach.
In this contribution I propose a contemporary reading of the ontological dimension of Max Scheler’s early phenomenology of sense perception. My examination will start with a brief informal explanation of this theory, and his scientific and philosophical sources. The second step will be the introduction of some elements of Formal Philosophy (FP): this piece of research will focus on N. B. Cocchiarella’s interpretation of FP and it will allow me to introduce the concept of a Philosophical Formal Ontology (PFO) in comparison with the computational one (CO). Finally, the third step will be the construction of a semi-formalized model of Scheler’s early phenomenology of sense perception. Here I will use a dynamic-epistemic version of the modal calculus KT5.
We argue that logical semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts: ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of and relations between objects of various ontological types. We will then show that accounting for these differences amounts to the integration of lexical and compositional semantics in one coherent framework, and to an embedding in our logical semantics of a strongly-typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. We will show that in such a framework a number of challenges in natural language semantics can be adequately and systematically treated.
Categorización, razonamiento y lenguaje. Modelos mentales en el corpus aristotelicum. Parte Primera
The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ plural reading of second-order quantifiers, for the notion of plurality is much more general, not only of that set, but also of class. In fact, by showing that a plurality is equivalent to sub-sets of a power set, the notion of plurality comes to suffer a loss of generality. Despite of this equivalence result, I maintain that Boolos’ formal semantics does not committ (directly) second-order languages (theories) to second-order entities (and to set theory), contrary to standard semantics. Further, such an equivalence result provides a rationale for many criticisms to Boolos’ formal semantics, in particular those by Resnik and Parsons against its alleged ontological innocence and on its Platonistic presupposition. The key set-theoretic notion involved in the equivalence proof is that of many-valued function. But, first, I will provide a clarification of the philosophical context and theoretical grounds of the genesis of Boolos’ formal semantics.
Formal Representation of Knowledge deals with the construction of real world models taken from a certain domain, which enables automatic reasoning and interpretation. These formal models, called also ontologies, are used to offer formal semantics (forms interpretable by machine) to all kinds of information. Ontology building in Computer Science is tightly connected to its philosophical and logical concepts. Organizing objects into categories is a very important part of knowledge representation. Even though the interaction with the world is made based on individual objects, most of the reasoning is done based on objects’ categories. Categorical formation is an intellectual issue even though its objects are not pieces of the intellectual world. As a matter of fact these objects stand at the top of the perceptive world in such a way that they look totally apart from their real structures. Standing at this practical level it is important to cite that the moment of object categorization is a pure formal process. For a business company these categories must reflect business’ concepts and rules, its logic and the conventions between the business itself and the organizations it cooperates with. In this paper we build a basis on the formalization of the categorical system. These formalizations are contemporary tools which the Albanian businesses must embrace in order for them to function properly.
DOI: 10.5901/ajis.2014.v3n1p427
In a seminal work published in 1952, "The chemical basis of morphogenesis" - considered as the true start point of the modern theoretical biology -, A. M. Turing established the core of what today we call "natural computation" in biological systems, intended as self-organizing dynamic systems. In this contribution we show that the "intentionality", i.e., the "relation-to-object" characterizing biological morphogenesis and cognitive intelligence, as far as it is formalized in the appropriate ontological interpretation of the modal calculus (formal ontology), can suggest a solution of the reference problem that formal semantics is in principle unable to offer, because of Gödel and Tarski theorems. Such a solution, that is halfway between the "descriptive" (Frege) and the "causal" (Kripke) theory of reference, can be implemented only in a particular class of self-organizing dynamic systems, i.e., the dissipative chaotic systems characterizing the "semantic information processing" in biological and neural systems.
Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors (operators forming terms from formulas). A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to standard first-order logic, and shows that the proof-theoretic meanings of both logics coincide. The paper criticizes Frege’s original regimentation of quantified sentences of natural language, and argues for advantages of the proposed variant.
In a seminal work published in 1952, “The chemical basis of morphogenesis”, A. M. Turing established the core of what today we call “natural computation” in biological systems, intended as self-organizing dissipative systems. In this contribution we show that a proper implementation of Turing’s seminal idea cannot be based on diffusive processes, but on the coherence states of condensed matter according to the dissipative Quantum Field Theory (QFT) principles. This foundational theory is consistent with the intentional approach in cognitive neuroscience, as far as it is formalized in the appropriate ontological interpretation of the modal calculus (formal ontology). This interpretation is based on the principle of the “double saturation” between a singular argument and its predicate that has its dynamical foundation in the principle of the “doubling of the degrees of freedom” between a brain state and the environment, as an essential ingredient of the mathematical formalism of dissipative QFT.
http://www.mrtc.mdh.se/~gdc/work/AISB-IACAP-2012/NaturalComputingProceedings-2012-06-22.pdf
Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory
that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an
integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional
contents of our concepts are “object”-ified, and by which an analysis of predication with intensional verbs can be given.
Through a second nominalization of the common names that are part of conceptual realism’s theory of reference (via quantifier
phrases), the theory also accounts for both plural reference and predication and mass noun reference and predication. Finally,
a separate nexus of predication based on natural kinds and the natural properties and relations nomologically related to those
natural kinds, is also an integral part of the framework of conceptual realism.
Turing presented a general representation scheme by which to achieve
artificial intelligence - unorganised machines. Significantly, these were a
form of discrete dynamical system and yet such representations remain
relatively unexplored. Further, at the same time as also suggesting that
natural evolution may provide inspiration for search mechanisms to design
machines, he noted that mechanisms inspired by the social aspects of learning
may prove useful. This paper presents initial results from consideration of
using Turing's dynamical representation within an unconventional substrate -
networks of Belousov-Zhabotinsky vesicles - designed by an imitation-based,
i.e., cultural, approach. Turing's representation scheme is also extended to
include a fuller set of Boolean functions at the nodes of the recurrent
networks.
This paper examines al-Fārābī's logical thought within its Arabico-Islamic historical background and attempts to conceptualize what this background contributes to his logic. After a brief exposition of al-Fārābī's main problems and goals, I shall attempt to reformulate the formal structure of Arabic linguistics (AL) in terms of the ontological and formal characteristics that Arabic logic is built upon. Having discussed the competence of al-Fārābī in the history of AL, I will further propose three interrelated theses about al-Fārābī's logic, in terms of which I will attempt to redefine it: the logico-linguistic conception, the project of logicization, and nuclear logic. The final question that will arise is how Aristotle's logic could be built upon AL, which has a nature contrary to logic. The present paper also contributes to examining our traditional research habits in Arabic studies.
The Ontological Square is a categorial scheme that combines two metaphysical distinctions: that between types (or universals) and tokens (or particulars) on the one hand, and that between characters (or features) and their substrates (or bearers) on the other hand. The resulting four-fold classification of things comprises particular substrates, called substances, universal substrates, called kinds, particular characters, called modes or moments, and universal characters, called attributes. Things are joined together in facts by primitive ontological ties or nexus. This article describes a logic that is meant to capture the basic intuitions behind the Ontological Square. Given a minimal
correspondence between atomic logical form and ontological structure, the commitment to nexus as a distinct ontological category
entails a rehabilitation of copulae as ties of predication. Thus, the Logic of the Ontological Square is a copula calculus
rather than a predicate calculus; its soundness and completeness can be established with respect to a model akin to a so-called
first-order semantics for standard second-order logic.
Ontology has been one of the hottest topic issues in artificial intelligence, knowledge engineering, especially in information process. In this paper, we propose an ontology-driven information retrieval (IR) system used for mining the interesting patterns in the domain of customers' complaints of mobile communication services. As the primary research of ontology model itself is about concept, properties of concept, relations between concepts etc, out of question ontology model considers the semantic relationships of the rich document content. Therefore ontology-driven information retrieval system can conform to the thought mode of human being unlike the keyword-based system that ignores the semantic relationships between words. Applying the proposed IR system to the given domain can make the managers of mobile communication companies retrieve the customers' complaints information more precisely and hence make decisions more reasonably
A new argument structure based on defeasible class-inclusion transitivity (DCIT) is proposed as a generalizable structure for evaluating probative relevancy determinations in litigation across typical
evidentiary fact patterns. The general applicability for deductive inferences can be seen through the use of Sommers term-functor
logic (TFL) principles to regiment premises into a DCIT structure. Its generalizability for inductive and presumptive (e.g.
plausibilistic) inferences can be demonstrated by translating a variety of informal logic structures (e.g. Toulmin, argument
schemes, Wigmorean charts and conventional box and arrow diagrams) into a DCIT argument structure.Aproper use of a DCIT structure
demonstrates whether the item of evidence offered to be admitted in the trial and the ultimate probandum of the case (e.g.
the defendant is guilty of murder) are linked within a single structurally correct argument. A DCIT perspective also provides
a coherent metaphorical explanation of the concepts of probative force, probative weight, linked and convergent premises and
inference.
The purpose of this paper is twofold: (i) we argue that the structure of commonsense knowledge must be discovered, rather than
invented; and (ii) we argue that natural language, which is the best known theory of our (shared) commonsense knowledge, should itself
be used as a guide to discovering the structure of commonsense knowledge. In addition to suggesting a systematic method to the
discovery of the structure of commonsense knowledge, the method we propose seems to also provide an explanation for a number of
phenomena in natural language, such as metaphor, intensionality, and the semantics of nominal compounds. Admittedly, our ultimate
goal is quite ambitious, and it is no less than the systematic ‘discovery’ of a well-typed ontology of commonsense knowledge, and the
subsequent formulation of the long-awaited goal of a meaning algebra.
In this paper we suggest a typed compositional seman-tics for nominal compounds of the form [Adj Noun] that models adjectives as higher-order polymorphic functions, and where types are assumed to represent concepts in an ontology that reflects our commonsense view of the world and the way we talk about it in or-dinary language. In addition to [Adj Noun] compounds our proposal seems also to suggest a plausible explana-tion for well known adjective ordering restrictions.
Predication has been a central, if not the central, issue in philosophy since at least the time of Plato and Aristotle. Different theories of predication have in fact been the basis of a number of philosophical controversies in both metaphysics and epistemology, not the least of which is the problem of universals. In what follows we shall be concerned with what traditionally have been the three most important types of theories of universals, namely, nominalism, conceptualism, and realism, and with the theories of predication which these theories might be said to determine or characterize.
A conceptual theory of the referential and predicable concepts used in basic speech and mental acts is described in which singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are given a uniform account. The theory includes an intensional realism in which the intensional contents of predicable and referential concepts are represented through nominalized forms of the predicate and quantifier phrases that stand for those concepts. A central part of the theory distinguishes between active and deactivated referential concepts, where the latter are represented by nominalized quantifier phrases that occur as parts of complex predicates. Peter Geach's arguments against theories of general reference in Reference and Generality are used as a foil to test the adequacy of the theory. Geach's arguments are shown to either beg the question of general as opposed to singular reference or to be inapplicable because of the distinction between active and deactivated referential concepts.
During the last thirty years or so the practice has grown up among logicians of attributing the project of a universal character to Leibniz alone among seventeenth century thinkers. This attribution is to be found, for instance, in L. S. Stebbing’s Modern Introduction to Logic,1in Cohen and Nagel’s Introduction to Logic and Scientific Method,2 in M. Black’s Nature of Mathematics,3 in J. H. Woodger’s Axiomatic Method in Biology,4 and in 0. Neurath’s introductory article in the International Encyclopaedia of Unified Science.
5 And it dates, I suspect, from the publication of C. I. Lewis’s Survey of Symbolic Logic in 1918. Lewis mentioned that Leibniz acknowledged a debt in this connexion to Raymond Lully, Athanasius Kircher, George Dalgarno and John Wilkins. But he considered their writings contained “little which is directly to the point”.6 In this Lewis was obviously right with regard to Leibniz’s conception of a calculus of reasoning, but wrong, as I shall try to show, with regard to the project of a universal character, which seems in fact to have been an intellectual commonplace in seventeenth century Western Europe. This somewhat neglected by-way of philosophical history is worth a brief review, I think, not only in order to fix more precisely the respect in which Leibniz was the only seventeenth century precursor of modern symbolic logicians, but also because it draws attention to an early widespread philosophical muddle about the cónstruction of artificial languages.
A formal ontology is both a theory of logical form and a metaphysical theory about the ontological structure of the world. What makes it a theory of logical form is that different ontological categories or modes of being are represented in it by different logico-grammatical categories. It is specified in this regard by what might be called an ontological grammar that determines how the expressions of those logico-grammatical categories can be meaningfully combined so as to represent different ontological aspects of the world.
Answering Schröder’s criticisms of Begriffsschrift, Frege states that, unlike Boole’s, his logic is not a calculus ratiocinator, or not merely a calculus ratiocinator, but a lingua characterica.1 If we come to understand what Frege means by this opposition, we shall gain a useful insight into the history of logic.
The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular terms. We argue against Quine's view that predicate quantifiers can be given a referential interpretation only if the entities predicates stand for on such an interpretation are the same as the classes (assuming extensionality) that nominalized predicates denote as singular terms. Quine's alternative of giving predicate quantifiers only a substitutional interpretation is compared with a constructive version of conceptual realism, which with a logic of nominalized predicates is compared with Quine's description of conceptualism as a ramified theory of classes. We argue against Quine's implicit assumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's class Platonism.
The most important background factor in the development of twentieth-century logic has received insufficient attention in the literature. This factor is a largely tacit contrast between ways of looking at the relation of language and its logic to reality. I have called them the idea of language as the universal medium and the idea of language as calculus.1 I shall also refer the two traditions representing these two respective ideas as the universalist tradition and as the model-theoretical tradition.
Knowledge representation in Artificial Intelligence (AI) involves more than the representation of a large number of facts or beliefs regarding a given domain, i.e. more than a mere listing of those facts or beliefs as data structures. It may involve, for example, an account of the way the properties and relations that are known or believed to hold of the objects in that domain are organized into a theoretical whole—such as the way different branches of mathematics, or of physics and chemistry, or of biology and psychology, etc., are organized, and even the way different parts of our commonsense knowledge or beliefs about the world can be organized. But different theoretical accounts will apply to different domains, and one of the questions that arises here is whether or not there are categorial principles of representation and organization that apply across all domains regardless of the specific nature of the objects in those domains. If there are such principles, then they can serve as a basis for a general framework of knowledge representation independently of its application to particular domains. In what follows I will give a brief outline of some of the categorial structures of conceptual realism as a formal ontology. It is this system that I propose we adopt as the basis of a categorial framework for knowledge representation.
INTRODUCTION PART ONE. THE ELEMENTS I. LOGIC Quantification and identity Virtual classes Virtual relations II. REAL CLASSES Reality, extensionality, and the individual The virtual amid the real Identity and substitution III. CLASSES OF CLASSES Unit classes Unions, intersections, descriptions Relations as classes of pairs Functions IV. NATURAL NUMBERS Numbers unconstrued Numbers construed Induction V. ITERATION AND ARITHMETIC Sequences and iterates The ancestral Sum, product, power PART TWO. HIGHER FORMS OF NUMBER VI. REAL NUMBERS Program. Numerical pairs Ratios and reals construed Existential needs. Operations and extensions VII. ORDER AND ORDINALS Transfinite induction Order Ordinal numbers Laws of ordinals The order of the ordinals VIII. TRANSFINITE RECURSION Transfinite recursion Laws of transfinite recursion Enumeration IX. CARDINAL NUMBERS Comparative size of classes The SchrOder-Bernstein theorem Infinite cardinal numbers X. THE AXIOM OF CHOICE Selections and selectors Further equivalents of the axiom The place of the axiom PART THREE. AXIOM SYSTEMS XI. RUSSELL'S THEORY OF TYPES The constructive part Classes and the axiom of reducibility The modern theory of types XII. GENERAL VARIABLES AND ZERMELO The theory of types with general variables Cumulative types and Zermelo Axioms of infinity and others XIII. STRATIFICATION AND ULTIMATE CLASSES "New foundations" Non-Cantorian classes. Induction again Ultimate classes added XIV. VON NEUMANN'S SYSTEM AND OTHERS The von Neumann-Bernays system Departures and comparisons Strength of systems SYNOPSIS OF FIVE AXIOM SYSTEMS LIST OF NUMBERED FORMULAS BIBLIOGRAPHICAL REFERENCES INDEX
Thesis (Ph. D.)--University of Massachusetts, 1984. Includes bibliographical references (p. 470-477). Photocopy of typescript.
The Theory of Models
- J W Addison
- L Henkin
- A Tarski
Addison, J. W., L. Henkin and A. Tarski: 1965, The Theory of Models, Amsterdam: North-Holland.
The Structure of Appcarance
- N Goodman
The Principles of Mathematics, 2nd edn., with a new intro
- B P Russell
Tarski: 1965, The Theory of Models
- J W Addison
- L Henkin
Begriffsschrift, A Formula Language, Modeled upon that of Arithmetic, for Pure Thought
- G Frege
- G. Frege
A World of Individuals
- N Goodman
- N. Goodman
Reference and Generality
- P Geach
- P. Geach