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Logic and Logical Philosophy
Journal Prestige (SJR): 0.387
Number of Followers: 5  

  This is an Open Access Journal Open Access journal
ISSN (Print) 1425-3305 - ISSN (Online) 2300-9802
Published by UMK Homepage  [22 journals]
  • Acknowledgments

    • PubDate: Wed, 07 Dec 2022 00:00:00 +010
  • An Introduction to the Special Issue: Logics and Their Interpretations II

    • Authors: Henrique Antunes; Damian Szmuc
      PubDate: Wed, 07 Dec 2022 00:00:00 +010
  • Local Applications of Logics via Model-Theoretic Interpretations

    • Authors: Carlos Benito-Monsalvo
      Abstract: This paper analyses the notion of ‘interpretation’, which is often tied to the semantic approach to logic, where it is used when referring to truth-value assignments, for instance. There are, however, other uses of the notion that raise interesting problems. These are the cases in which interpreting a logic is closely related to its justification for a given application. The paper aims to present an understanding of interpretations that supports the model-theoretic characterization of validity to the detriment of the proof-theoretic one. This is done by making use of the hierarchy of ST-related logics. Finally, a localist conception of logic is defended as the natural view stemming from the model-theoretic approach.
      PubDate: Sat, 09 Jul 2022 00:00:00 +020
  • Game Semantics, Quantifiers and Logical Omniscience

    • Authors: Bruno Ramos Mendonça
      Abstract: Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences (consequences for which epistemic closure certainly holds) from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], an expressive fragment of classical game semantics that weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of some first-order sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is needed to obtain a better solution of the problem. In this paper, I argue that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be formulated as follows: when inquiring after the truth-value of ∀xφ, an individual might be unaware of all substitutional instances this sentence accepts, but at least she must know that, if an element a is given, then ∀xφ holds only if φ(x/a) is true. This thesis accepts game-theoretic formalization in terms of a refinement of urn semantics. I maintain that the system so obtained (US+) affords an improved solution of the logical omniscience problem. To do this, I characterize first-order theoremhood in US+. As a consequence of this result, we will see that the ideal reasoner depicted by US+ only knows the validity of first-order formulas whose Herbrand witnesses can be trivially found, a fact that provides strong evidence that our refinement of urn semantics captures a relevant sense of logical obviousness.
      PubDate: Mon, 13 Jun 2022 00:00:00 +020
  • A Four-Valued Logical Framework for Reasoning About Fiction

    • Authors: Newton Peron; Henrique Antunes
      Abstract: In view of the limitations of classical, free, and modal logics to deal with fictional names, we develop in this paper a four-valued logical framework that we see as a promising strategy for modeling contexts of reasoning in which those names occur. Specifically, we propose to evaluate statements in terms of factual and fictional truth values in such a way that, say, declaring ‘Socrates is a man’ to be true does not come down to the same thing as declaring ‘Sherlock Holmes is a man’ to be so. As a result, our framework is capable of representing reasoning involving fictional characters that avoids evaluating statements according to the same semantic standards. The framework encompasses two logics that differ according to alternative ways one may interpret the relationships among the factual and fictional truth values.
      PubDate: Wed, 25 May 2022 00:00:00 +020
  • Relational Semantics for the Paraconsistent and Paracomplete 4-valued
           Logic PŁ4

    • Authors: Gemma Robles; Sandra M. López, José M. Blanco
      Abstract: The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases.
      PubDate: Sat, 23 Apr 2022 00:00:00 +020
  • Many-Valued Logics and Bivalent Modalities

    • Authors: Edson Bezerra; Giorgio Venturi
      Abstract: In this paper, we investigate the family LS0.5 of many-valued modal logics LS0.5's. We prove that the modalities of necessity and possibility of the logics LS0.5's capture well-defined bivalent concepts of logical validity and logical consistency. We also show that these modalities can be used as recovery operators.
      PubDate: Mon, 11 Apr 2022 00:00:00 +020
  • Beyond Mixed Logics

    • Authors: Joaquín Toranzo Calderón; Federico Pailos
      Abstract: In order to define some interesting consequence relations, certain generalizations have been proposed in a many-valued semantic setting that have been useful for defining what have been called pure, mixed and ordertheoretic consequence relations. But these generalizations are insufficient to capture some other interesting relations, like other intersective mixed relations (a relation that cannot be defined as a mixed relation, but only as the intersection of two mixed relations) or relations with a conjunctive (or, better, “universal”) interpretation for multiple conclusions. We propose a broader framework to define these cases, and many others, and to set a common background that allows for a direct compared analysis. At the end of the work, we illustrate some of these comparisons
      PubDate: Mon, 11 Apr 2022 00:00:00 +020
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