•  65
    A discrete duality between apartness algebras and apartness frames
    with Ivo Düntsch
    Journal 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.
  •  56
    Relational proof system for relevant logics
    Journal 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
  •  53
    Relational dual tableaux for interval temporal logics
    with David Bresolin and Joanna Golinska-Pilarek
    Journal 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
  •  49
    Relational proof systems for spatial reasoning
    with Joanna Golińska-Pilarek
    Journal of Applied Non-Classical Logics 16 (3-4): 409-431. 2006.
    We present relational proof systems for the four groups of theories of spatial reasoning: contact relation algebras, Boolean algebras with a contact relation, lattice-based spatial theories, spatial theories based on a proximity relation
  •  47
    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
  •  39
    Equational Reasoning in Non-Classical Logics
    with Marcelo Frias
    Journal of Applied Non-Classical Logics 8 (1-2): 27-66. 1998.
    ABSTRACT In this paper it is shown that a broad class of propositional logics can be interpreted in an equational logic based on fork algebras. This interpetability enables us to develop a fork-algebraic formalization of these logics and, as a consequence, to simulate non-classical means of reasoning with equational theories algebras
  •  39
    Logic For Reasoning About Knowledge
    Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (6): 559-572. 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
  •  39
    Modal Logics in the Theory of Information Systems
    Mathematical Logic Quarterly 30 (13-16): 213-222. 1984.
  •  31
    A hierarchy of modal logics with relative accessibility relations
    with Philippe Balbiani
    Journal of Applied Non-Classical Logics 9 (2-3): 303-328. 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
  •  30
    Duality via Truth: Semantic frameworks for lattice-based logics
    with Ingrid Rewitzky
    Logic 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
  •  28
    Logics of similarity and their dual tableaux. A survey
    In Giacomo Della Riccia, Didier Dubois & Hans-Joachim Lenz (eds.), Preferences and Similarities, Springer. pp. 129--159. 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.
  •  27
    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 non-classical logics are recalled. An example is given of a dual tableau proof of an equation which is RRA-valid, while not RA-valid.
  •  22
    Obituary—Helena Rasiowa
    Journal of Applied Non-Classical Logics 4 (2). 1994.
  •  21
    Dynamic logic with program specifications and its relational proof system
    Journal of Applied Non-Classical Logics 3 (2): 147-171. 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
  •  18
    Obituary Zdzislaw Pawlak (1926–2006)
    Journal of Applied Non-Classical Logics 17 (1): 7-8. 2007.
    No abstract
  •  18
    Dual tableau-based decision procedures for relational logics with restricted composition operator
    with Domenico Cantone and Marianna Nicolosi Asmundo
    Journal of Applied Non-Classical Logics 21 (2): 177-200. 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.
  •  17
    Foreword
    with Alberto Policriti and Andrzej Szalas
    Journal of Applied Non-Classical Logics 16 (3-4): 249-250. 2006.
    No abstract
  •  14
    Monoidal triangular norm logic MTL is the logic of left-continuous 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 MTL-formulas. We prove soundness and completeness of the system.
  •  8
    A Relational Formalisation Of Arbitrary Finite Valued Logics
    with B. Konikowska and C. Morgan
    Logic Journal of the IGPL 6 (5): 755-774. 1998.
    A method of developing a relational semantics and relational proof systems for many-valued logics based on finite algebras of truth values is presented. The method is applied to Rosser-Turquette logic, logics based on symmetric Heyting algebras with operators and a Post-style logic
  •  7
    Foreword
    Journal of Applied Non-Classical Logics 8 (1-2): 7-8. 1998.
  •  6
    International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers Harrie de Swart. Dual residua of a lattice join were ... The dual residua of well— known t-conorms Definition 2. ([28], [29]) A double residuated lattice ...
  •  5
    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
  •  1
  •  1
    Relational interpretation of modal logics
    Bulletin of the Section of Logic 17 (1): 2-10. 1988.
    The purpose of the present paper is to show that modal propositional logics can be interpreted in a logic based on relational calculus. We consider languages with necessity operators [R], where R is an accessibility relation expression representing an element of the algebra of binary relations with operations −,∪,∩, −1 , ◦. The relational logic is based on relational calculus enriched by operations of weakest prespecification and weakest postspecification introduced in Hoare and He Jifeng and inve…Read more
  • Treshold Logic
    Bulletin of the Section of Logic 1 (3): 20-27. 1972.
  • Three aspects of verisimilitude. Part II
    Bulletin of the Section of Logic 16 (4): 140-147. 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
  • Relational logics for formalization of database dependencies
    with Wojciech Buszkowski
    Bulletin of the Section of Logic 27. 1998.