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Alexander Bochman - One of the best experts on this subject based on the ideXlab platform.

Andrzej Pietruszczak - One of the best experts on this subject based on the ideXlab platform.

  • A Method of Generating Modal Logics Defining Jaśkowski’s Discussive D2 Consequence
    Logic Argumentation & Reasoning, 2014
    Co-Authors: Marek Nasieniewski, Andrzej Pietruszczak
    Abstract:

    Jaśkowski’s logic D 2 is usually understood as a set of discussive formulae. Studying Jaśkowski’s paper one can also find a Consequence Relation (the D 2 -Consequence). The logic D 2 was meant to express this Consequence Relation. Since the logic D 2 was formulated with the help of a modal logic, the Consequence Relation is also defined in the modal language. It is known that the logic D 2 can be defined by other modal logics than S5. A similar question arises as regards the Consequence Relation. In Nasieniewski and Pietruszczak (On modal logics defining Jaśkowski’s D2-Consequence. In: Tanaka K, Berto F, Mares E, Paoli F (eds) Paraconsistency: logic and applications. Logic, epistemology and the unity of science, chap 8, vol 26. Springer, Dordrecht/New York, pp 141–161, 2013) there are given modal logics other than S5 which define exactly the same Consequence Relation. In the present paper we try to develop a more general method of defining modal logics which also allow to define the D 2 -Consequence.

  • The axiomatization of Horst Wessel’s strict logical Consequence Relation
    Logic and Logical Philosophy, 2004
    Co-Authors: Andrzej Pietruszczak
    Abstract:

    In his book from 1984 Horst Wessel presents the system of strict logical Consequence Fs (see also (Wessel, 1979)). The author maintained that this system axiomatized the Relation |=s of strict logical Consequence between formulas of Classical Propositional Calculi (CPC). Let |= be the classical Consequence Relation in CPC. The Relation |=s is defined as follows: \phi |=s \psi iff \phi |= \psi, every variable from \psi occurs in \phi and neither \phi is a contradiction nor \psi is a tautology. Clearly, if \phi |=s \psi, then neither \phi is a tautology nor \psi is a contradiction. Intuitions connected with the Relation |=s were presented in (Wessel, 1984). The analysis of the Relation |=s is also carried out in (Pietruszczak, 2004). In the present paper we will show that the system Fs is not a complete axiomatization of the Relation |=s. Moreover, we will present the system VF s that is an «extension to completeness» of the Fs.

  • the axiomatization of horst wessel s strict logical Consequence Relation
    Logic and Logical Philosophy, 2004
    Co-Authors: Andrzej Pietruszczak
    Abstract:

    In his book from 1984 Horst Wessel presents the system of strict logical Consequence Fs (see also (Wessel, 1979)). The author maintained that this system axiomatized the Relation |=s of strict logical Consequence between formulas of Classical Propositional Calculi (CPC). Let |= be the classical Consequence Relation in CPC. The Relation |=s is defined as follows: \phi |=s \psi iff \phi |= \psi, every variable from \psi occurs in \phi and neither \phi is a contradiction nor \psi is a tautology. Clearly, if \phi |=s \psi, then neither \phi is a tautology nor \psi is a contradiction. Intuitions connected with the Relation |=s were presented in (Wessel, 1984). The analysis of the Relation |=s is also carried out in (Pietruszczak, 2004). In the present paper we will show that the system Fs is not a complete axiomatization of the Relation |=s. Moreover, we will present the system VF s that is an «extension to completeness» of the Fs.

  • The Consequence Relation preserving logical information
    Logic and Logical Philosophy, 2004
    Co-Authors: Andrzej Pietruszczak
    Abstract:

    Information is contained in statements and «flows» from their structure and meaning of expressions they contain. The information that flows only from the meaning of logical constants and logical structure of statements we will call logical information. In this paper we present a formal explication of this notion which is proper for sentences being Boolean combination of atomic sentences. 1 Therefore we limit ourselves to analyzing logical information flowing only from the meaning of truth-value connectives and logical structure of sentences connected with these connectives.

Ka-shu Wong - One of the best experts on this subject based on the ideXlab platform.

Gunther Gediga - One of the best experts on this subject based on the ideXlab platform.

Philip Kremer - One of the best experts on this subject based on the ideXlab platform.

  • SUPERVALUATION FIXED-POINT LOGICS OF TRUTH
    Journal of Philosophical Logic, 2008
    Co-Authors: Philip Kremer, Alasdair Urquhart
    Abstract:

    Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as Consequence Relation, is highly complex: it is not even analytic. We also consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a Consequence Relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived.

  • Some Supervaluation-based Consequence Relations
    Journal of Philosophical Logic, 2003
    Co-Authors: Philip Kremer, Michael Kremer
    Abstract:

    In this paper, we define some Consequence Relations based on supervaluation semantics for partial models, and we investigate their properties. For our main Consequence Relation, we show that natural versions of the following fail: upwards and downwards Lowenheim–Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting Consequence Relation.