Logic and Logical Philosophy 2022-08-09T15:05:09+02:00 Andrzej Pietruszczak Open Journal Systems <p><em>Logic and Logical Philosophy</em> is a journal chiefly devoted to philosophical logic and philosophy resulting from applying logical tools to philosophical problems. Other applications of logic to related disciplines are not excluded.</p> <p>Beginning with 2016, <em>Logic and Logical Philosophy</em> is being indexed and abstracted in Emerging Sources Citation Index in Clarivate Analytics products and services (<a href=";ISSN=1425-3305">Web of Science Master Journal List</a>). <em>LLP</em> is included in two categories: philosophy and logic. Clarivate Analytics launches Journal Citation Indicator (JCI) for 2021 in the 2021 Journal Citation Reports (JCR). JCI index for <em>LLP</em> is 1.09. This value gives <em>LLP</em> (<a href=";year=2020&amp;fromPage=%2Fjcr%2Fbrowse-journals&amp;SID=H3-JZyy6gg7XqbrX5s9l8oMfmuhCMBGuuKX-18x2dCrI6CaTt8clTPTpUU0DGKQx3Dx3DI5vvpjan6wPorHx2B3Pa4tWwx3Dx3D-WwpRYkX4Gz8e7T4uNl5SUQx3Dx3D-wBEj1mx2B0mykql8H4kstFLwx3Dx3D">link</a>): <br />• the third place in the category of logic: JCI rank 2/25, JCI quartile Q1, JCI percentile 94; <br />• the 60th place in the category of philosophy: JCI rank 60/320, JCI quartile Q1, JCI percentile 81.41.</p> <p><em>Logic and Logical Philosophy</em> has been indexed in the Scopus database since 2011. According to their 2021 results, Scopus CiteScore™ gives <em>LLP</em> the 83th percentile for a journal of philosophy (<a href="">link</a>).<br />Scimago Journal Rank 2021 (SJR = 0.762) has determined that <em>LLP</em> has status Q1 for a journal of philosophy, placing 40 among 667 journals <a href=";tip=sid&amp;clean=0"> (link)</a>.</p> Dynamic Probabilistic Entailment. Improving on Adams' Dynamic Entailment Relation 2021-09-09T23:35:13+02:00 Robert van Rooij Patricia Mirabile <p>The inferences of contraposition (A ⇒ C ∴ ¬C ⇒ ¬A), the hypothetical syllogism (A ⇒ B, B ⇒ C ∴ A ⇒ C), and others are widely seen as unacceptable for counterfactual conditionals. Adams convincingly argued, however, that these inferences are unacceptable for indicative conditionals as well. He argued that an indicative conditional of form A ⇒ C has assertability conditions instead of truth conditions, and that their assertability ‘goes with’ the conditional probability p(C|A). To account for inferences, Adams developed the notion of probabilistic entailment as an extension of classical entailment. This combined approach (correctly) predicts that contraposition and the hypothetical syllogism are invalid inferences. Perhaps less well-known, however, is that the approach also predicts that the unconditional counterparts of these inferences, e.g., modus tollens (A ⇒ C, ¬C ∴ ¬A), and iterated modus ponens (A ⇒ B, B ⇒ C, A ∴ C) are predicted to be valid. We will argue both by example and by calling to the results from a behavioral experiment (N = 159) that these latter predictions are incorrect if the unconditional premises in these inferences are seen as new information. Then we will discuss Adams’ (1998) dynamic probabilistic entailment relation, and argue that it is problematic. Finally, it will be shown how his dynamic entailment relation can be improved such that the incongruence predicted by Adams’ original system concerning conditionals and their unconditional counterparts are overcome. Finally, it will be argued that the idea behind this new notion of entailment is of more general relevance.</p> 2021-12-23T00:00:00+01:00 Copyright (c) 2021 Logic and Logical Philosophy Logics for Knowability 2021-06-04T10:47:57+02:00 Mo Liu Jie Fan Hans van Ditmarsch Louwe B. Kuijer <p>In this paper, we propose three knowability logics<strong> LK</strong>, LK<sup>−</sup>, and <strong>LK</strong><sup>=</sup>. In the single-agent case, <strong>LK</strong> is equally expressive as arbitrary public announcement logic <strong>APAL</strong> and public announcement logic <strong>PAL</strong>, whereas in the multi-agent case, <strong>LK</strong> is more expressive than <strong>PAL</strong>. In contrast, both <strong>LK</strong><sup>−</sup> and LK<sup>=</sup> are equally expressive as classical propositional logic <strong>PL</strong>. We present the axiomatizations of the three knowability logics and show their soundness and completeness. We show that all three knowability logics possess the properties of Church-Rosser and McKinsey. Although<strong> LK</strong> is undecidable when at least three agents are involved,<strong> LK</strong><sup>−</sup> and<strong> LK</strong><sup>=</sup> are both decidable.</p> 2021-12-08T00:00:00+01:00 Copyright (c) 2021 Logic and Logical Philosophy S5-Style Non-Standard Modalities in a Hypersequent Framework 2021-08-31T14:55:54+02:00 Yaroslav Petrukhin <p>The aim of the paper is to present some non-standard modalities (such as non-contingency, contingency, essence and accident) based on <strong>S5</strong>-models in a framework of cut-free hypersequent calculi. We also study negated modalities, i.e. negated necessity and negated possibility, which produce paraconsistent and paracomplete negations respectively. As a basis for our calculi, we use Restall's cut-free hypersequent calculus for <strong>S5</strong>. We modify its rules for the above-mentioned modalities and prove strong soundness and completeness theorems by a Hintikka-style argument. As a consequence, we obtain a cut admissibility theorem. Finally, we present a constructive syntactic proof of cut elimination theorem.</p> 2021-12-16T00:00:00+01:00 Copyright (c) 2021 Logic and Logical Philosophy Topology of Modal Propositions Depicted by Peirce’s Gamma Graphs: Line, Square, Cube, and Four-Dimensional Polyhedron 2021-08-26T21:37:42+02:00 Jorge Alejandro Flórez <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>This paper presents the topological arrangements in four geometrical figures of modal propositions and their derivative relations by means of Peirce's gamma graphs and their rules of transformation. The idea of arraying the gamma graphs in a geometric and symmetrical order comes from Peirce himself who in a manuscript drew two cubes in which he presented the derivative relations of some (but no all) gamma graphs. Therefore, Peirce's insights of a topological order of gamma graphs are extended here backwards from the cube to the line and the square; and then forwards from the cube to the four-dimensional polyhedron.</p> </div> </div> </div> 2021-11-30T00:00:00+01:00 Copyright (c) 2021 Logic and Logical Philosophy Analysis of Penrose’s Second Argument Formalised in DTK System 2021-03-25T01:46:00+01:00 Antonella Corradini Sergio Galvan <p>This article aims to examine Koellner’s reconstruction of Penrose’s second argument – a reconstruction that uses the <strong>DTK</strong> system to deal with Gödel’s disjunction issues. Koellner states that Penrose’s argument is unsound, because it contains two illegitimate steps. He contends that the formulas to which the <strong>T-intro</strong> and <strong>K-intro</strong> rules apply are both indeterminate. However, we intend to show that we can correctly interpret the formulas on the set of arithmetic formulas, and that, as a consequence, the two steps become legitimate. Nevertheless, the argument remains partially inconclusive. More precisely, the argument does not reach a result that shows there is no formalism capable of deriving all the true arithmetic propositions known to man. Instead, it shows that, if such formalism exists, there is at least one true non-arithmetic proposition known to the human mind that we cannot derive from the formalism in question. Finally, we reflect on the idealised character of the <strong>DTK</strong> system. These reflections highlight the limits of human knowledge, and, at the same time, its irreducibility to computation.</p> 2021-12-16T00:00:00+01:00 Copyright (c) 2021 Logic and Logical Philosophy Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability 2020-05-13T02:00:00+02:00 Pawel Pawlowski Rafal Urbaniak <p>BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not.</p> 2021-11-29T00:00:00+01:00 Copyright (c) 2021 Logic and Logical Philosophy