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Publications (571)
The notion of negation is basic to any formal or informal logical system. When any such system is presented to us, it is presented either as a system without negation or as a system with some form of negation. In both cases, we are supposed to know intuitively whether there is no negation in the system or whether the form of negation presented in t...
This position paper connects the areas and communities of abstract argumentation and attack-defence trees in the area of security. Both areas deal with attacks, defence and support and both areas rely on applications dealing with human aggressive activities. The unifying idea we use in this paper is to regard arguments as AND-OR attack trees as pro...
This paper offers a Talmudic norms solution to the paradox of the heap. The claim is that the paradox arises because philosophers use the wrong language to discuss it. We need a language about objects which is capable of expressing not only the declarative properties of the object (such as being a heap) but also how the object/heap was constructed....
The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axioma...
The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axioma...
We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make avail...
Aim/Purpose: Finding and tagging citation on an ancient Hebrew religious document. These documents have no structured citations and have no bibliography. Background: We look for common patterns within Hebrew religious texts. Methodology: We developed a method that goes over the texts and extracts sentences con-taining the names of three famous auth...
This article presents a unique method in text and data mining for finding the era, i.e., mining temporal data, in which an anonymous author was living. Finding this era can assist in the examination of a fake document or extracting the time period in which a writer lived. The study and the experiments concern Hebrew, and in some parts, Aramaic and...
Suppose we are given a monadic theory T about the constants x and y. So T is built up in classical logic from monadic predicates {P1, P2, ...} and the classical connectives and the quantifiers and possibly the equality symbol =. For example the theory T may have in it P (x) and ¬P (y). We now add to the theory the revision input x = y. The new theo...
Formal argumentation is one of the most popular approaches in modern logic and reasoning. The theory of abstract argumentation introduced by Dung in 1995 has shifted the focus from the internal structure of arguments to relations among arguments, and temporal dynamics for abstract argumentation was proposed by Barringer, Gabbay and Woods in 2005. I...
This eighteenth volume of the acclaimed Handbook of Philosophical Logic includes many contributors who are among the most famous leading figures of applied philosophical logic of our time. Coverage includes deontic logic, practical reasoning, homogeneous and heterogeneous logical proportion, and talmudic logic. Overall, it will appeal to students,...
This study is trying to determine the time-frame in which the author of a given document lived. The documents are rabbinic documents written in Hebrew-Aramaic languages. The documents are undated and do not contain a bibliographic section, which leaves us with an interesting challenge. To do this, we define a set of key-phrases and formulate variou...
We study instantiated abstract argumentation frames of the form $(S,R,I)$,
where $(S,R)$ is an abstract argumentation frame and where the arguments $x$ of
$S$ are instantiated by $I(x)$ as well formed formulas of a well known logic,
for example as Boolean formulas or as predicate logic formulas or as modal
logic formulas. We use the method of conce...
This chapter contains basic notation, definitions and results.
This chapter presents the basic ideas and problems of defeasible inheritance.
Multiplicative laws of size and the related interpolation property of nonmonotonic logics are important notions of independence, and thus a case of restricted influence, the central topic of this book.
This is the central chapter of the book, where the authors bring together the main concepts presented earlier.
This chapter discusses some problems with an approach to the Talmudic law of Kal Vachomer. This law is based on an assumption of regularity of the world. The authors show that straightforward induction is impossible, as one may have to “look backward” to lower levels of a construction.
The authors’ ambition is to construct a special preferential structure in Chap. 11 based on ideas from inheritance, defaults and theory revision, and this chapter is a thorough introduction to preferential structures.
This chapter offers a short introduction to Reiter defaults.
Here the authors introduce deontic logic and contrary-to-duty obligations.
The strategy described here is an illustration of the fact that one may describe graded information by either a relation on the information or the semantics itself, as in preferential structures, or by a relation on the truth values. Here the authors take the latter approach to solve problems with contrary-to-duty obligations.
This chapter treats probabilistic and abstract independence for sets and general function sets.
This chapter explains theory revision, theory contraction and conditionals.
The authors introduce Edelman’s theory of organization of the brain and the resulting phenomena; these are important for the further development of theories of common sense reasoning, in particular concerning concept formation and abstract constructions.
This book deals with a problem that has been discussed quite a lot, both in the academic and the halachic literature, the problem of partitioning. The fundamental and well-known partition problem in the Talmud is the partition of lost property (“Two hold a garment”) found in Baba Metzia 2a, and its generalisation (“n hold a garment”). The Talmud al...
This report documents the program and the outcomes of Dagstuhl Perspectives Workshop 15362 "Present and Future of Formal Argumentation".
The goal of this Dagstuhl Perspectives Workshop was to gather the world leading experts in formal argumentation in order to develop a SWOT (Strength, Weaknesses, Opportunities, Threats)
analysis of the current s...
Here the authors motivate the book and provide a summary of its contents.
In this book the authors present new results on interpolation for nonmonotonic logics, abstract (function) independence, the Talmudic Kal Vachomer rule, and an equational solution of contrary-to-duty obligations. The chapter on formal construction is the conceptual core of the book, where the authors combine the ideas of several types of nonmonoton...
We translate the argumentation networks ${\cal A}=(S, R)$ into a theory $D$
of intuitionistic logic, retaining $S$ as the domain and using intuitionistic
negation to model the attack $R$ in ${\cal A}$: the attack $xRy$ is translated
to $x\to\neg y$. The intuitionistic models of $D$ characterise the complete
extensions of ${\cal A}$.
The reduction o...
We translate the argumentation networks ${\cal A}=(S, R)$ into a theory $D$ of intuitionistic logic, retaining $S$ as the domain and using intuitionistic negation to model the attack $R$ in ${\cal A}$: the attack $xRy$ is translated to $x\to\neg y$. The intuitionistic models of $D$ characterise the complete extensions of ${\cal A}$. The reduction o...
We discuss properties of what we call argumentation systems with disjunctive attacks, where we have an argument x x attacking a set of arguments H H, without specifically attacking any specific y ∈ H y∈H. In other words, x x attacks the conjunction ∧ y ∈ H y ∧y∈Hy.
This volume deals with issues already discussed in volumes eight and nine: Analysis and Synthesis of concepts. So far we have assumed binary logic, i.e., either something is true or it is false. Now we leave this dichotomous approach, and discover that an extension to multi-valued logic (fuzzy logic) and quantum states helps to solve problems left...
We add strong negation $N$ to classical logic and interpret the attack
relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a
corresponding object level (using $N$ only) classical theory for each
argumentation network and show that the classical models of this theory
correspond exactly to the complete extensions of the argumentat...
We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical theory for each argumentation network and show that the classical models of this theory correspond exactly to the complete extensions of the argumentat...
In the last few years, several publications discussed a new method of matrix completion, called matrix abduction, which is particularly useful in the context of Talmudic logic and legal ruling systems in general. Given a matrix \(\mathbf{A}\) with entries that are either in \(\{0,1\}\) or blank, the method allows us to decide whether each blank ent...
A new method of abduction, matrix abduction, has been introduced in Abraham, M., Gabbay, D., Schild, U.: Talmudic argumentum a fortiori inference rule (Kal Vachomer) using matrix abduction. Studia Logica 92(3), 281–364 (2009). This method describes the Kal Vachomer and the Binyan Abh rules by using microscopic parameters which exist in the inputs o...
There is a generic way to add any new feature to a system. It involves 1)
identifying the basic units which build up the system and 2) introducing the
new feature to each of these basic units.
In the case where the system is argumentation and the feature is
probabilistic we have the following. The basic units are: a. the nature of the
arguments inv...
In this study, we try to determine the time-frame in which the author of a given document lived. The discussed documents are rabbinic documents written in the Hebrew, Aramaic and Yiddish languages. The documents are usually undated and do not contain a bibliographic section, which leaves us with an interesting challenge to determine the desired tim...
It is shown that I/O logic can be based on intuitionistic logic instead of classical logic. More specifically, it is established that, when going intuitionistic, a representation theorem is still available for three of the four (unconstrained) original I/O operations. The trick is to see a maximal consistent set as a saturated one. The axiomatic ch...
In this research, we identify the era in which the author of the given
document(s) lived. For rabbinic documents written in Hebrew-Aramaic, which
are usually undated and do not contain any bibliographic section, this problem
is important. The aim of this research is to find in which years an author was
born and died, based on his documents and...
Given an argumentation network with initial values to the arguments, we look
for algorithms which can yield extensions compatible with such initial values.
We find that the best way of tackling this problem is to offer an iteration
formula that takes the initial values and the attack relation and iterates a
sequence of intermediate values that even...
In abstract argumentation arguments are just points in a network of attacks: they do not hold premisses, conclusions or internal structure. So is there a meaningful way in which two arguments, belonging possibly to different attack graphs, can be said to be equivalent? The paper argues for a positive answer and, interfacing methods from modal logic...
One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. Hasi...
We develop a model of abduction in abstract argumentation, where changes to
an argumentation framework act as hypotheses to explain the support of an
observation. We present dialogical proof theories for the main decision
problems (i.e., finding hypothe- ses that explain skeptical/credulous support)
and we show that our model can be instantiated on...
In this paper we provide a Beth-Reichenbach (BR) semantics capable of analyzing the miners puzzle. We augment the BR-semantics with reactive arrows, obtaining a new semantic that we call ReBR-semantics, and sharpen our analysis to the miners puzzle. We further extend the ReBR-semantics with actions to obtain our final ReBRA-semantics, capable of mo...
A linguistic analysis of deontic paradoxes can be used to further develop deontic logic. In this paper we provide a Beth-Reichenbach semantics to analyze deontic paradoxes, and we illustrate it on the single agent decision problem of the miners scenario. We also introduce extensions with reactive arrows and actions, which can be used to give a ling...
The aim of this article is to construct a deontic logic in which the free choice postulate [11] would be consistent and all the implausible result mentioned in [5] will be blocked. To achieve this we first developed a new theory of action. Then we build a new deontic logic in which the deontic action operator and the deontic proposition operator ar...
Plato's theory of forms and Aristotle's Hylomorphism form a foundational bifurcation at the source of western philosophy. From a Jurisprudential and Talmudic point of view, assessing the status of objects and actions obligatory in Halacha can be clarified when assessed through this dual view of obligations to abstract ideal forms or concrete earthl...
We apply the equational approach to logic to define numerical equational semantics and consequence relations for contrary to duty obligations, thus avoiding some of the traditional known paradoxes in this area. We also discuss the connection with abstract argumentation theory. Makinson and Torre’s input output logic and Governatori and Rotolo’s log...
In this article we show how to model a range of notions in the context of delegation and revocation applied to security scenarios.
We demonstrate how a range of delegation–revocation models and policies may be represented in pictorial form and formally
represented in terms of reactive Kripke models and a first-order policy specification language. W...
In this book we deal with combinations of concepts defining individuals in
the Talmud. Consider for example Yom Kippur and Shabbat. Each concept
has its own body of laws. Reality forces us to combine them when they
occur on the same day. This is a case of "Identity Merging".
As the combined body of laws may be inconsistent, we need a belief
revi...
This article is about busting loops in abstract argumentation networks. We propose several approaches to how to deal with networks which have loops (such as even or odd cycles) and get new extensions which are ‘in’, ‘out’ extensions, with no undecided elements.
Given an argumentation network with initial values to the arguments, we look for a numerical algorithm yielding extensions compatible with such initial values. We offer an iteration schema that takes the initial values of the nodes and follows the attack relation producing a sequence of intermediate values that eventually becomes stable leading to...
This article concerns the merging of argumentation systems. We propose an equational approach to this problem by considering
an augmented network containing the arguments and attacks of all systems to be merged and then associating a numerical weight
to each of the components of the augmented network. The weights are calculated based on how the com...
argumentation networks have been studied in two directions
• Investigate their semantics in detail. This has lead to the study of extensions, dealing with loops, connections with classical logic, the notions joint and disjunctive attacks, and especially what concerns us here, the Equational approach and the ASPIC instantiation approach.
• Generali...
Trust is used to minimise the uncertainty in the interactions of the agents especially in case of conflicting information from different sources. Besides conflicts among information there can also be conflicts about the trust attributed to the information sources. In this paper, we discuss how to reason about trust using argumentation theory, so to...
We present a unifying semantical and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic, namely approximations in which the number of nested applications of a single structural rule, representing the classical Principle of Bivalence, is bounded above by a fixed natural number. These approximations provide a...
Ordinary dynamic action logics deal with states and actions upon states. The actions can be deterministic or non-deterministic, but it is always assumed that the possible results of the actions are clear cut.Talmudic logic deals with actions (usually legally meaningful actions which can change the legal status of an entity) which depend on the futu...
This book returns to the discussion in Volume 1 on analogy and induction and analyses their substance. The first part distinguishes between two kinds of logic: one kind based on union of the common features, and the other kind based on synthesis of different features. In the second part of the book we propose a formal scheme for synthesis of concep...
Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been sh...
Deontic logic is the logic of obligation and permission. In the literature it has mainly been studied in terms of a list of problems and that is the way we chose to present it in this section. There are three main categories of problems. The first category is concerned with the nature of norms. The second category concerns phenomena of conflict, vi...
Ordinary Kripke models are not reactive. When we evaluate (test/measure) a formula A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process. This is reminiscent of game theoretic se...
In this paper, we propose a logic of argumentation for the specification and verification (LA4SV) of requirements on Dung’s abstract argumentation frameworks. We distinguish three kinds of decision problems for argumentation verification, called extension verification, framework verification, and specification verification respectively. For example...
The collection in this special issue contains mainly papers on reactive Kripke semantics and on argumentation. This overview says a few words about how these papers fit in the general picture.
This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple. Given a system with states and the possibility of transitions moving from one state to another, we can naturally imagine a path beginning at an initial state and moving along the path...
The collection in this special issue contains mainly papers on reactive Kripke semantics and on argumentation. This overview says a few words about how these papers fit in the general picture.
The notion of reactive graph generalises the one of graph by allowing the base accessibility relation to change when its edges are traversed. Can we represent these more general structures using points and arrows? We prove this can be done by introducing higher order arrows: the switches. The possibility of expressing the dependency of the future s...
Cayrol and Lagasquie-Schiex introduce bipolar argumentation frameworks by introducing a second relation on the arguments for representing the support among them. The main drawback of their approach is that they cannot encode defeasible support, for instance they cannot model an attack towards a support relation. In this paper, we introduce a way to...
This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator–prey ecological networks, flow networ...
This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the “extensions” of the network. This approach is very general and includes the Caminada labelling as a special case, as well as ma...
In my papers [2,7], I modelled the Chisholm paradox and generally Chisholm like sequences of contrary to duty obligations by using Reactive Kripke models [4]. Reactive Kripke frames have two types of arrows: ordinary single arrows x → y indicating accessibility relations and double arrows of the form \(( u \to v) \twoheadrightarrow ( x \to y)\), in...
We consider a generalised Chisholm set of contrary to duty obligations (CTD) of the form
$$ O q_0 $$ and for i = 0,…, n we have the CTD is
$$ \begin{array} {l} q_i\to O q_{i+1}\\ \neg q_i \to O \neg q_{i+1} \end{array} $$ and the facts ±q
j
for some j ∈ J ⊆ {0,1,…, n + 1}. Note that for the case of n = 1 and fact ¬q
0 we have the Chisholm paradox....
Norm change is one of the main challenges for normative reasoning. This discussion paper presents some novel informal and semi-formal ideas regarding the nature and formalization of norm change. First, we contrast the second-order nature of norm change with the first-order nature of obligation change. Second, we discuss how to change the normative...
We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic
predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with
respect to the intended relational semantics is established.
KeywordsDynamic logic–Substructural...
This book studies the Talmudic approach to Delegation. We develop logical models for the basic Talmudic views of delegation. The Talmudic approaches to the relationships between the Principal and his Agent/Delegate are fundamentally very logical, and deal with questions like chains of delegations, transfer of power, cancellations, death, irresponsi...
We consider conditionals of the form A ⇒ B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.
Three main aspects will be investigated:
Inverse causality from future to past, where a future condition can influen...
The problem of interpolation is a classical problem in logic. Given a consequence relation |~ and two formulas and ψ with |~ ψ we try to find a “simple" formula α such that |~ α |~ ψ. “Simple" is defined here as “expressed in the common language of and ψ". Non-monotonic logics like preferential logics are often a mixture of a non-monotonic part wit...
We suggest a general logical framework for causal dynamic reasoning. As a first step, we introduce a uniform structural formalism and assign it two kinds of semantics, abstract dynamic models and relational models. The corresponding completeness results are proved. As a second step, we extend the structural formalism to a two-sorted state-transitio...
We introduce a family of new equational semantics for argumentation networks
which can handle odd and even loops in a uniform manner. We offer one version
of equational semantics which is equivalent to CF2 semantics, and a better
version which gives the same results as traditional Dung semantics for even
loops but can still handle odd loops.
We introduce a reactive variant of SDL (standard deontic logic): SDLR1 (reactive standard deontic logic). Given a Kripkean view on the semantics of SDL in terms of directed graphs where arrows → represent the accessibility relation between worlds, reactive models add two elements:
arrows → are labelled as ‘active’ or ‘inactive’, and double arrows ↠...
An equational approach is used to give semantics to negation as failure. We offer an Equational Calculus and in it we define a new completion for programs with negation as failure in the body of clauses. This approach is compared with other approaches in the literature and a connection is established with argumentation theory.
In this paper we follow ideas from our Equational approach to argumentation, [3,4], and develop the Equational approach to Logic programs. We regard a logic program P as a template for generating a system of equations Eq(P), where the literals are considered variables ranging over the unit interval [0, 1], and where the solutions to the equations g...
Philosophy of Linguistics investigates the foundational concepts and methods of linguistics, the scientific study of human language. This groundbreaking collection, the most thorough treatment of the philosophy of linguistics ever published, brings together philosophers, scientists and historians to map out both the foundational assumptions set dur...
Philosophy of Economics investigates the foundational concepts and methods of economics, the social science that analyzes the production, distribution and consumption of goods and services. This groundbreaking collection, the most thorough treatment of the philosophy of economics ever published, brings together philosophers, scientists and historia...