
Interpolation and Definability: Modal and Intuitionistic LogicsOxford University Press UK. 2005.This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous worldrenowned Oxford Logic Guides, which contains Michael Dumm…Read more

Extending the Curry {Howard {Tait interpretation to linear, relevant and other logicsJournal of Symbolic Logic 56 112940. 1992.

8REVIEWSManydimensional modal logics: Theory and applicationsBulletin of Symbolic Logic 11 (1): 7778. 2005.

2Argumentation modelling of the Toulmin schemeStudia Logica 93 (23): 297354. 2009.In this paper, we introduce the methodology and techniques of metaargumentation to model argumentation. The methodology of metaargumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of metaargumentation applies Dung’s theory o…Read more

13Computation with run time skolemisation (NProlog part 3)Journal of Applied NonClassical Logics 3 (1): 93128. 1993.No abstract

45Contrary to time conditionals in Talmudic logicArtificial Intelligence and Law 20 (2): 145179. 2012.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 influence a legal event in the past (this is a man made causality).Comparison with similar features in modern law.New types of temporal logics arising from mod…Read more

57Obligations and prohibitions in Talmudic deontic logicArtificial Intelligence and Law 19 (23): 117148. 2011.This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg A$ This is not the case in the Talmud f…Read more

40Labelled resolution for classical and nonclassical logicsStudia Logica 59 (2): 179216. 1997.Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for nonclassical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tru…Read more

9A Sequence of Decidable Finitely Axiomatizable Intermediate Logics with the Disjunction PropertyJournal of Symbolic Logic 39 (1). 1974.

28Equational approach to argumentation networksArgument and Computation 3 (23). 2012.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 many other socalled network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational appr…Read more

20Undecidability of modal and intermediate firstorder logics with two individual variablesJournal of Symbolic Logic 58 (3): 800823. 1993.

44Naming worlds in modal and temporal logicJournal of Logic, Language and Information 11 (1): 2965. 2002.In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y)which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order to use…Read more

116A theory of hypermodal logics: Mode shifting in modal logic (review)Journal of Philosophical Logic 31 (3): 211243. 2002.A hypermodality is a connective □ whose meaning depends on where in the formula it occurs. The paper motivates the notion and shows that hypermodal logics are much more expressive than traditional modal logics. In fact we show that logics with very simple K hypermodalities are not complete for any neighbourhood frames

32Fibred semantics and the weaving of logics part 1: Modal and intuitionistic logicsJournal of Symbolic Logic 61 (4): 10571120. 1996.This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L…Read more

45NeuralSymbolic Cognitive ReasoningSpringer. 2009.Humans are often extraordinary at performing practical reasoning. There are cases where the human computer, slow as it is, is faster than any artificial intelligence system. Are we faster because of the way we perceive knowledge as opposed to the way we represent it? The authors address this question by presenting neural network models that integrate the two most fundamental phenomena of cognition: our ability to learn from experience, and our ability to reason from what has been learned. This b…Read more

17Compiled Labelled Deductive Systems a Uniform Presentation of NonClassical LogicsInstitute of Physics/Research Studies Press. 2004.K. Broda, Dov M. Gabbay, Alessandra Russo (all computing or computer science, Imperial College, London) and LuÍs C. Lamb (Informatics, UFRGS, Brazil) argue that though the many families of logic may seem to differ in their logical nature, it is possible to provide them with a unifying logical framework whenever their semantics is axiomatizable in firstorder logic. They provide such a framework based on the labeled deductive system methodology, and demonstrate how it works in such families as no…Read more

5Do we really need tenses other than future and past?In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Semantics From Different Points of View, Springer Verlag. pp. 1520. 1979.

6Languages, Metalanguages and METATEM, A Discussion PaperLogic Journal of the IGPL 4 (2): 255272. 1996.Metalanguages are vital to the development and usage of formal systems, and yet the nature of metalanguages and associated notions require clarification. Here we attempt to provide a clear definition of the requirements for a language to be a metalanguage, together with consideration of issues of proof theory, model theory and interpreters for such a language

37Logical Analysis of the Talmudic Rules of General and Specific (KlalimuPratim)History and Philosophy of Logic 32 (1): 4762. 2011.This article deals with a settheoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP)

13Investigations in Modal and Tense Logics with Application to Problems in Philosophy and LinguisticsJournal of Symbolic Logic 44 (4): 656657. 1979.

59A general theory of structured consequence relationsTheoria 10 (2): 4978. 1995.There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional nonmonotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical nonmonotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief re…Read more

57Reactive preferential structures and nonmonotonic consequenceReview of Symbolic Logic 2 (2): 414450. 2009.We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. These are networks with arrows recursively leading to other arrows etc. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can the strong coherence properties of preferential structures by higher arrows, that is, arrows, w…Read more

12Completeness properties of heyting's predicate calculus with respect to re modelsJournal of Symbolic Logic 41 (1): 8194. 1976.