
63Cut and payJournal of Logic, Language and Information 15 (3): 195218. 2006.In this paper we study families of resource aware logics that explore resource restriction on rules; in particular, we study the use of controlled cutrule and introduce three families of parameterised logics that arise from different ways of controlling the use of cut. We start with a formulation of classical logic in which cut is noneliminable and then impose restrictions on the use of cut. Three CutandPay families of logics are presented, and it is shown that each family provides an approx…Read more

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

76Combining Temporal Logic SystemsNotre Dame Journal of Formal Logic 37 (2): 204232. 1996.This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component onedimensional temporal logics to the resulting combined twodimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of…Read more

376Analysis of the Talmudic Argumentum A Fortiori Inference Rule using Matrix AbductionStudia Logica 92 (3): 281364. 2009.We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of nondeductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix with entries in {0,1}, we allow for one or more blank squares in the matrix, say $a_{i,j} =?.$ The method allows us to decide whether to declare $a_{i,j} = 0$ or $a_{i,j} = 1$ or $a_{i,j} =?$ undecided. This algorithmic method is then applied to modelling several legal and practical…Read more

43Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]Synthese 187 (2): 623660. 2012.This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of ContrarytoDuties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study i…Read more

23On Kreisel's notion of validity in post systemsStudia Logica 35 (3). 1976.This paper investigates various interpretations of HPC (Heyting's predicate calculus) and mainly of HPC0 (Heyting's propositional calculus) in Post systems.§1 recalls some background material concerning HPC including the Kripke and Beth interpretations, and later sections study the various interpretations available.

22Annotation Theories over Finite GraphsStudia Logica 93 (2): 147180. 2009.In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories^ can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotati…Read more

8Parsing natural language using LDS: a prototypeLogic Journal of the IGPL 5 (5): 647671. 1997.This paper describes a prototype implementation of a Labelled Deduction System for natural language interpretation, where interpretation is taken to be the process of understanding a natural language utterance. The implementation models the process of understanding whgap dependencies in questions and relative clauses for a fragment of English. The paper is divided in three main sections. In Section 1, we introduce the basic architecture of the system. Section 2 outlines a prototype implementati…Read more

9GoalDirected Proof TheoryKluwer Academic. 2000.Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in nonclassical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goaldirected provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of nonclassical systems, covering intuitionistic, inte…Read more

An intuitionistic basis for nonmonotonic reasoningIn Philippe Smets (ed.), NonStandard Logics for Automated Reasoning, Academic Press. 1988.

417Abductive reasoning in neuralsymbolic systemsTopoi 26 (1): 3749. 2007.Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of nonsymbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypotheticodeductive reasoning. In this paper we start to bridge the gap between the symbolic and subsymbolic approaches to abdu…Read more

46Fibring Argumentation FramesStudia Logica 93 (2): 231295. 2009.This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theo…Read more

47Labelled Deductive SystemsOxford University Press. 1996.This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.

63An irreflexivity lemma with applications to axiomatizations of conditions on tense framesIn U. Mönnich (ed.), Aspects of Philosophical Logic, Dordrecht. pp. 6789. 1981.

37Size and logicReview of Symbolic Logic 2 (2): 396413. 2009.We show how to develop a multitude of rules of nonmonotonic logic from very simple and natural notions of size, using them as building blocks

822. Filtration Structures and the Cut Down Problem for AbductionIn Kent A. Peacock & Andrew D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods, University of Toronto Press. pp. 398417. 2005.

32Fibred Security LanguageStudia Logica 92 (3): 395436. 2009.We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of firstorder formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language both for classical and intuitionistic fragment), we then prov…Read more

59A Comment on Work by Booth and CoauthorsStudia Logica 94 (3): 403432. 2010.Booth and his coauthors have shown in [2], that many new approaches to theory revision (with fixed K ) can be represented by two relations, , where is a subrelation of < . They have, however, left open a characterization of the infinite case, which we treat here.

1The Handbook of the History of Logic, vol. 7: Logic and the Modalities in the Twentieth Century (edited book)Elsevier Press. 2006.

18Dung’s Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce–Quine DaggerLogica Universalis 5 (2): 255318. 2011.In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ${\neg, \wedge, \vee, \to}$ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logi…Read more

10Łukasiewicz Logic: From Proof Systems To Logic ProgrammingLogic Journal of the IGPL 13 (5): 561585. 2005.We present logic programming style “goaldirected” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goaldirected calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants