
2Semantical Considerations for Modal Logics by Saul A. KripkeJournal of Symbolic Logic 34 (3): 501501. 1969.

7Belief contraction, antiformulae and resource overdraft: Part II deletion in resource unbounded logicsIn S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science, Kluwer Academic Publisher. pp. 291326. 2004.

Sampling Logic and Argumentation Networks: A ManifestoJournal of the Indian Council of Philosophical Research 27 (2). 2010.

33Montague Type Semantics for Modal Logics with Propositional QuantifiersZeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1): 245249. 1971.

35Algorithmic proof methods and cut elimination for implicational logics part I: Modal implicationStudia Logica 61 (2): 237280. 1998.In this work we develop goaldirected deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility.…Read more

55Two 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

50Uncertainty Rules in Talmudic ReasoningHistory and Philosophy of Logic 32 (1): 6369. 2011.The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps …Read more

41Logical modes of attack in argumentation networksStudia Logica 93 (23): 199230. 2009.This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The networkbased system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the socalled rulebas…Read more

44A normal logic that is complete for neighborhood frames but not for Kripke framesTheoria 41 (3): 148153. 1975.

53Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: OverviewStudia Logica 93 (23). 2009.In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics (of extensions) to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the m…Read more

28Decidability of some intuitionistic predicate theoriesJournal of Symbolic Logic 37 (3): 579587. 1972.

41A Metamodel of Access Control in a Fibred Security LanguageStudia Logica 92 (3): 437477. 2009.The issue of representing access control requirements continues to demand significant attention. The focus of researchers has traditionally been on developing particular access control models and policy specification languages for particular applications. However, this approach has resulted in an unnecessary surfeit of models and languages. In contrast, we describe a general access control model and a logicbased specification language from which both existing and novel access control models may…Read more

111Direct deductive computation on discourse representation structuresLinguistics and Philosophy 17 (4). 1994.

9Representation of the Montague Semantics as a Form of the Suppes Semantics with Applications to the Problem of the Introduction of the Passive Voice, the Tenses, and Negation as TransformationsIn Jaakko Hintikka (ed.), Approaches to Natural Language, D. Reidel Publishing. pp. 395409. 1973.

75Adding a temporal dimension to a logic systemJournal of Logic, Language and Information 1 (3): 203233. 1992.We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic like soundness, completeness, …Read more

38Philosophy of economics (edited book)North Holland. 2012.This volume serves as a detailed introduction for those new to the field as well as a rich source of new insights and potential research agendas for those already engaged with the philosophy of economics.

2Products of modal logics and tensor products of modal algebrasJournal of Applied Logic 12 (4): 570583. 2014.

31Craig interpolation theorem for intuitionistic logic and extensions part IIIJournal of Symbolic Logic 42 (2): 269271. 1977.