
27Relational logics and their applicationsIn Harrie de Swart, Ewa Orlowska, Gunther Smith & Marc Roubens (eds.), Theory and Applications of Relational Structures as Knowledge Instruments II: International Workshops of COST Action 274, TARSKI, 20022005, Selected Revised Papers, Springer. pp. 125161. 2006.Logics of binary relations corresponding, among others, to the class RRA of representable relation algebras and the class FRA of full relation algebras are presented together with the proof systems in the style of dual tableaux. Next, the logics are extended with relational constants interpreted as point relations. Applications of these logics to reasoning in nonclassical logics are recalled. An example is given of a dual tableau proof of an equation which is RRAvalid, while not RAvalid.

List of participants 17 Robert K. Meyer (Camberra, Australia) Barbara Morawska (Gdansk, Poland) Daniele Mundici (Milan, Italy)Logic and Logical Philosophy 7 16. 2001.

A proof system for fork algebras and its applications to reasoning in logics based on intuitionismLogique Et Analyse 150 151152. 1995.

5Logics in Artificial Intelligence: European Workshop, Jelia '96, Evora, Portugal, September 30  October 3, 1996, Proceedings (review)Springer Verlag. 1996.This book presents the refereed proceedings of the Sixth European Workshop on Logics in Artificial Intelligence, JELIA '96, held in Evora, Portugal in September/October 1996. The 25 revised full papers included together with three invited papers were selected from 57 submissions. Many relevant aspects of AI logics are addressed. The papers are organized in sections on automated reasoning, modal logics, applications, nonmonotonic reasoning, default logics, logic programming, temporal and spatial …Read more

8A Relational Formalisation Of Arbitrary Finite Valued LogicsLogic Journal of the IGPL 6 (5): 755774. 1998.A method of developing a relational semantics and relational proof systems for manyvalued logics based on finite algebras of truth values is presented. The method is applied to RosserTurquette logic, logics based on symmetric Heyting algebras with operators and a Poststyle logic

3Logics in Artificial Intelligence: Proceedings of European Workshop, Jelia '96, Évora, Portugal, September 30October 3, 1996 (edited book, review)Springer. 1996.

49Relational proof systems for spatial reasoningJournal of Applied NonClassical Logics 16 (34): 409431. 2006.We present relational proof systems for the four groups of theories of spatial reasoning: contact relation algebras, Boolean algebras with a contact relation, latticebased spatial theories, spatial theories based on a proximity relation

Logic of vague conceptsBulletin of the Section of Logic 11 (34): 115126. 1982.This paper contains a logic enabling us to reason in the presence of vague ness phenomena. We consider an epistemological vagueness of concepts caused by the unavailability of total information about a continuous world which we describe in observational terms. Lack of information is manifested by the existence of borderline cases for concepts. Since we are unable to perceive concepts exactly, we cannot establish a sharp boundary between an extension of a concept and its complement. Some results…Read more

Three aspects of verisimilitude. Part IIBulletin of the Section of Logic 16 (4): 140147. 1987.In the following two sections we propose ordering relations for which the material for comparison of theories of concepts the theories deal with. The relations refer to what is called concept analysis. In the present section we introduce relations enabling us to compare theories from the point of view of the following aspect: How well the theories in question classify objects into positive and negative instances of concepts. Classiﬁcations of objects provided by a theory can be correct or incorr…Read more

Three aspects of verisimilitude. Part IBulletin of the Section of Logic 16 (3): 96103. 1987.One of the generalizations of R. W´ojcicki’s concept of referential matrix is socalled pseudoreferential matrix. G. Malinowski, who introduced that concept, also considers a particular case of pseudoreferential matrices called discrete pseudoreferential matrices. In this note we want to show how any generalized matrix determines a semantically equivalent discrete pseudoreferential matrix.

18Obituary Zdzislaw Pawlak (1926–2006)Journal of Applied NonClassical Logics 17 (1): 78. 2007.No abstract

39Logic For Reasoning About KnowledgeZeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (6): 559572. 1989.One of the important issues in research on knowledge based computer systems is development of methods for reasoning about knowledge. In the present paper semantics for knowledge operators is introduced. The underlying logic is developed with epistemic operators relative to indiscernibility. Facts about knowledge expressible in the logic are discussed, in particular common knowledge and joint knowledge of n group of agents. Some paradoxes of epistemic logic are shown to be eliminated in the given…Read more

A Logic With Relevant InplicationBulletin of the Section of Logic 16 (1): 3943. 1987.In Orlowska and Weingartner an approach to relevance was proposed based on the notion of sematic relevance criterion which is understood as a binary relation in the set of predicates of a language under consideration. Some general properties were investigated of sets of formulas relevant with respect to relevance criteria or sets of relevance criteria. Informally, a predicate P is relevant for a predicate Q whenever some information about instances of Q can be derived from information about inst…Read more

18Dual tableaubased decision procedures for relational logics with restricted composition operatorJournal of Applied NonClassical Logics 21 (2): 177200. 2011.We consider fragments of the relational logic RL(1) obtained by posing various constraints on the relational terms involving the operator of composition of relations. These fragments allow to express several non classical logics including modal and description logics. We show how relational dual tableaux can be employed to provide decision procedures for each of them.

14Dual tableau for monoidal triangular norm logic MTLFuzzy Sets and Systems 162 (1). 2011.Monoidal triangular norm logic MTL is the logic of leftcontinuous triangular norms. In the paper we present a relational formalization of the logic MTL and then we introduce relational dual tableau that can be used for verification of validity of MTLformulas. We prove soundness and completeness of the system.

6Relational formalization of temporal logicsIn Georg Schurz (ed.), Advances in Scientific Philosophy, . pp. 24143. 1991.

Logic For Reasoning About KnowledgeBulletin of the Section of Logic 16 (1): 2636. 1987.One of the important issues in research on knowledge based computer systems is development of methods for reasoning about knowledge. In the present paper semantics for knowledge operators is introduced. The underlying logic is developed with epistemic operators relative to indiscernibility. Facts about knowledge expressible in the logic are discussed, in particular common knowledge and joint knowledge of n group of agents. Some paradoxes of epistemic logic are shown to be eliminated in the given…Read more

21Dynamic logic with program specifications and its relational proof systemJournal of Applied NonClassical Logics 3 (2): 147171. 1993.ABSTRACT Propositional dynamic logic with converse and test, is enriched with complement, intersection and relational operations of weakest prespecification and weakest postspecification. Relational deduction system for the logic is given based on its interpretation in the relational calculus. Relational interpretation of the operators ?repeat? and ?loop? is given

6International Workshops of COST Action 274, TARSKI, 20022005, Selected Revised Papers Harrie de Swart. Dual residua of a lattice join were ... The dual residua of well— known tconorms Definition 2. ([28], [29]) A double residuated lattice ...

Three Aspects of Verisimilitude'Bulletin of the Section of Logic 16 (3): 96106. 1987.One of the generalizations of R. W´ojcicki’s concept of referential matrix is socalled pseudoreferential matrix . G. Malinowski, who introduced that concept, also considers a particular case of pseudoreferential matrices called discrete pseudoreferential matrices . In this note we want to show how any generalized matrix determines a semantically equivalent discrete pseudoreferential matrix

Interpretation of dynamic logic and its extensions in the relational calculusBulletin of the Section of Logic 18 132137. 1989.

28Logics of similarity and their dual tableaux. A surveyIn Giacomo Della Riccia, Didier Dubois & HansJoachim Lenz (eds.), Preferences and Similarities, Springer. pp. 129159. 2008.We present several classes of logics for reasoning with information stored in information systems. The logics enable us to cope with the phenomena of incompleteness of information and uncertainty of knowledge derived from such an information. Relational inference systems for these logics are developed in the style of dual tableaux.

31A hierarchy of modal logics with relative accessibility relationsJournal of Applied NonClassical Logics 9 (23): 303328. 1999.ABSTRACT In this paper we introduce and investigate various classes of multimodal logics based on frames with relative accessibility relations. We discuss their applicability to representation and analysis of incomplete information. We provide axiom systems for these logics and we prove their completeness
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Mathematics 