9 found
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  1.  83
    Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics.Arnon Avron, Jonathan Ben-Naim & Beata Konikowska - 2007 - Logica Universalis 1 (1):41-70.
    . The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general (...)
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  2.  17
    Multi-Valued Calculi for Logics Based on Non-Determinism.Arnon Avron & Beata Konikowska - 2005 - Logic Journal of the IGPL 13 (4):365-387.
    Non-deterministic matrices are multiple-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. We consider two different types of semantics which are based on Nmatrices: the dynamic one and the static one . We use the Rasiowa-Sikorski decomposition methodology to get sound and complete proof systems employing finite sets of mv-signed formulas for all propositional logics based on such structures with either of the above (...)
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  3.  42
    A Logic for Reasoning About Relative Similarity.Beata Konikowska - 1997 - Studia Logica 58 (1):185-226.
    A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented.
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  4.  37
    Proof Systems for Reasoning About Computation Errors.Arnon Avron & Beata Konikowska - 2009 - Studia Logica 91 (2):273-293.
    In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a (...)
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  5.  8
    Two Over Three: A Two-Valued Logic for Software Specification and Validation Over a Three-Valued Predicate Calculus.Beata Konikowska - 1993 - Journal of Applied Non-Classical Logics 3 (1):39-71.
  6.  29
    Decomposition Proof Systems for Gödel-Dummett Logics.Arnon Avron & Beata Konikowska - 2001 - Studia Logica 69 (2):197-219.
    The main goal of the paper is to suggest some analytic proof systems for LC and its finite-valued counterparts which are suitable for proof-search. This goal is achieved through following the general Rasiowa-Sikorski methodology for constructing analytic proof systems for semantically-defined logics. All the systems presented here are terminating, contraction-free, and based on invertible rules, which have a local character and at most two premises.
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  7.  29
    A Two-Valued Logic for Reasoning About Different Types of Consequence in Kleene's Three-Valued Logic.Beata Konikowska - 1990 - Studia Logica 49 (4):541 - 555.
    A formal language of two-valued logic is developed, whose terms are formulas of the language of Kleene's three-valued logic. The atomic formulas of the former language are pairs of formulas of the latter language joined by consequence operators. These operators correspond to the three sensible types of consequence (strong-strong, strong-weak and weak-weak) in Kleene's logic in analogous way as the implication connective in the classical logic corresponds to the classical consequence relation. The composed formulas of the considered language are built (...)
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  8.  16
    A Multimodal Logic for Reasoning About Complementarity.Ivo Düntsch & Beata Konikowska - 2000 - Journal of Applied Non-Classical Logics 10 (3-4):273-301.
    ABSTRACT Two objects o1, o2 of an information system are said to be complementary with respect to attribute a if α(o1) = -α(o2), where α(o) is the set of values of attribute a assigned to o. They are said to be complementary with respect to a set of attributes A if they are complementary with respect to each attribute α ε A. A multi-modal logical language for reasoning about complementarity relations is presented, with modalities [A] and ?A? parameterised by subsets (...)
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  9.  5
    A Decompositional Deduction System for a Logic Featuring Inconsistency and Uncertainty.Beata Konikowska - 2005 - Journal of Applied Non-Classical Logics 15 (1):25-44.
    The paper discusses a four-valued propositional logic FOUR≤, similar to Belnap's logic, which can be used to describe incomplete or inconsistent knowledge. In addition to the two classical logical values tt, ff, FOUR≤ features also two nonclassical values: ⊥, representing incomplete information, and ⊤, representing inconsistency. The nonclassical values are incomparable, and together with the classical ones they form a diamond-shaped lattice L4 known from Belnap's logic, which underlies the semantics of FOUR≤. The set of connectives contains those of Belnap's (...)
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