“The Heritage of Jerzy Łoś’s Philosophical Logic and the Polish Question”. An Introduction to the Volume

In the introduction, we discuss the inadequate reception of Polish scientists and scholars in the world of scientific and academic ideas. This nonreception can be attributed to the tragic historical situation of the country – the Hecatomb suffered by Poland. The philosophical logic heritage of Jerzy Łoś is one such forgotten discovery. The present volume is devoted to this very heritage as well as its reception. The four works printed herein are discussed in the introduction. Although they deal with different problems and their approach to the problem varies (some are of a historical nature while others propose some scientific activities), they all have one thing in common: the use of realisation operator. The operator is a logical connective that makes it possible to express various ideas. The realisation operator was introduced by Jerzy Łoś.In the introduction, we discuss the poor reception of Polish scientists and scholars in the world of scientific and academic ideas. This non-reception can be attributed to the tragic historical situation of the country – the Hecatomb suffered by Poland. The philosophical logic heritage of Jerzy Łoś is one such forgotten discovery. The present volume is devoted to this very heritage as well as its reception. The four works printed herein are discussed in the introduction. Although they deal with different problems and their approach to the problem varies (some are of a historical nature while others propose some scientific activities), they all have one thing in common: the use of  realisation operator. The operator is a logical connective that makes it possible to express various ideas. The realisation operator was introduced by Jerzy Łoś

David Makinson, "Bridges from Classical to Nonmonotonic Logic", King’s College Publications, London, 2005

Book Reviews: David Makinson, "Bridges from Classical to Nonmonotonic Logic", King’s College Publications, London, 2005, pp. 216, ISBN 1-904987-00-

Construction of tableaux for classical logic: Tableaux as combinations of branches, branches as chains of sets

The paper is devoted to an approach to analytic tableaux for propositional logic, but can be successfully extended to other logics. The distinguishing features of the presented approach are:(i) a precise set-theoretical description of tableau method; (ii) a notion of tableau consequence relation is defined without help of a notion of tableau, in our universe of discourse the basic notion is a branch;(iii) we define a tableau as a finite set of some chosen branches which is enough to check; hence, in our approach a tableau is only a way of choosing a minimal set of closed branches;(iv) a choice of tableau can be arbitrary, it means that if one tableau starting with some set of premisses is closed in the defined sense, then every branch in the power set of the set of formulas, that starts with the same set, is closed

Completeness of Minimal Positional Calculus

In the article "Podstawy analizy metodologicznej kanonów Milla" [2] Jerzy Łoś proposed an operator that refered sentences to temporal moments. Let us look, for example, at a sentence ‘It is raining in Toruń’. From a logical point of view it is a propositional function, which does not have any logical value, unless we point at a temporal context from a fixed set of such contexts. If the sentence was considered today as a description of a state of affairs, it could be true. If it was considered yesterday, it could be false. 1 The operator enables us to connect any sentence p with any temporal context t. Such a complex sentence we read as: a sentence p is realized at a temporal context t (a point of time, an interval of some kind, etc)

Relating Logic and Relating Semantics. History, Philosophical Applications and Some of Technical Problems

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the language of relating logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue.KKKKKKKK

Axiomatization of BLRI Determined by Limited Positive Relational Properties

In the paper a generalised method for obtaining an adequate axiomatic system for any relating logic expressed in the language with Boolean connectives and relating implication (BLRI), determined by the limited positive relational properties is studied. The method of defining axiomatic systems for logics of a given type is called an algorithm since the analysis allows for any logic determined by the limited positive relational properties to define the adequate axiomatic system automatically, step-by-step. We prove in the paper that the algorithm really works and we show how it can be applied to BLRI

On Logic of Strictly-Deontic Modalities. A Semantic and Tableau Approach

Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values under which we predicate the deontic qualifications. By taking this aspect into account, we arrive at a logical system which preserves laws proper to a deontic logic but where the standard paradoxes of deontic logic do not arise. It is a logic of strictly-deontic modalities DR

Applications of Relating Semantics: From non-classical logics to philosophy of science

Here, we discuss logical, philosophical and technical problems associated to relating logic and relating semantics. To do so, we proceed in three steps. The first step is devoted to providing an introduction to both relating logic and relating semantics. We discuss this problem on the example of different languages. Second, we address some of the main research directions and their philosophical applications to non-classical logics, particularly to connexive logics. Third, we discuss some technical problems related to relating semantics, and its application to philosophy of science, language and pragmatics

Jerzy Łoś Positional Calculus and the Origin of Temporal Logic

Most accounts, including leading textbooks, credit Arthur Norman Prior with the invention of temporal (tense logic). However, (i) Jerzy Łoś delivered his version of temporal logic in 1947, several years before Prior; (ii) Henrk Hiż’s review of Łoś’s system in Journal of Symbolic Logic was published as early as 1951; (iii) there is evidence to the effect that, when constructing his tense calculi, Prior was aware of Łoś’s system. Therefore, although Prior is certainly a key figure in the history tense logic, as well as modal logic in general, it should be accepted both in the literature that temporal logic was invented by Jerzy Łoś

Boolean Connexive Logics: Semantics and tableau approach

In this paper we define a new type of connexive logics which we call Boolean connexive logics. In such logics negation, conjunction and disjunction behave in the classical, Boolean way. We determine these logics through application of the relating semantics. In the final section we present a tableau approach to the discussed logics