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35Modal Logics in the Theory of Information SystemsMathematical Logic Quarterly 30 (13-16): 213-222. 1984.
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47Dual Tableaux: Foundations, Methodology, Case StudiesSpringer. 2011.The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions).…Read more
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64A discrete duality between apartness algebras and apartness framesJournal of Applied Non-Classical Logics 18 (2-3): 213-227. 2008.Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of (Bridges et al., 2003), and we prove a discrete duality for them.
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1Interpretation of relevant logics in a logic of ternary relationsBulletin of the Section of Logic 19 (No2): 39-49. 1990.
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50Relational dual tableaux for interval temporal logicsJournal of Applied Non-Classical Logics 16 (3-4). 2006.Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between intervals an…Read more
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Relational logics for formalization of database dependenciesBulletin of the Section of Logic 27. 1998.
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51Relational proof system for relevant logicsJournal of Symbolic Logic 57 (4): 1425-1440. 1992.A method is presented for constructing natural deduction-style systems for propositional relevant logics. The method consists in first translating formulas of relevant logics into ternary relations, and then defining deduction rules for a corresponding logic of ternary relations. Proof systems of that form are given for various relevant logics. A class of algebras of ternary relations is introduced that provides a relation-algebraic semantics for relevant logics
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29Duality via Truth: Semantic frameworks for lattice-based logicsLogic Journal of the IGPL 13 (4): 467-490. 2005.A method of defining semantics of logics based on not necessarily distributive lattices is presented. The key elements of the method are representation theorems for lattices and duality between classes of lattices and classes of some relational systems . We suggest a type of duality referred to as a duality via truth which leads to Kripke-style semantics and three-valued semantics in the style of Allwein-Dunn. We develop two new representation theorems for lattices which, together with the exist…Read more
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |