Tomasz Jarmużek

Nicolaus Copernicus University | umk · Departament of Logic

Some ideas of relating semantics for connexive logic (including modal connexive logic). They were presented more than two years ago in Kyoto University. In the presentation I see some mistakes, but in general ideas seem to be promising. Few of them have been already realized (see the publications). Most is waiting for examination.

In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the...

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 direc...

In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: $$\mathbf {D}$$ D (Dependence Logic), $$\mathbf {DD}$$ DD (Dual Dependence Logic), $$\mathbf {Eq}$$ Eq (Logic of Equality of Content), $$\mathbf {S}$$ S (Symmetric Relatedness Logic) and $$\mathbf {R}$$ R (Nonsymmetric Relatedness Logic) (Epstein in The semant...

We set out a general methodology for producing tableau systems for syl-logistic logics via a tableau metatheory that provides general and formal notions for different tableau syllogistic systems that vary by semantics or formulae. Moreover, by dint of these general notions, some facts, independent of their applications to a particular syllogistic l...

In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodaliza...

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic bringing it about that . These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules o...

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. we will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem....

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable (weak permission understood as an absence of prohibition) or uncontroversially valid (strong permission within sys...

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 m...

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 paper is about Boolean connexive logics (BCL) and modal Boolean connexive logics. We propose some axiomatizations of systems closed under demodalization conditions and negation. In general, we explain the main tool we use: relating semantics which seems tailor-made for contra-classical logics.

he initiative of this Special Issue of the Bulletin of the Section of Logicwas born during one of the Chinese-Polish Workshops on Applied Logicand is connected with the developing collaboration between Chinese andPolish logicians. On the one hand, Poland has a long and strong presencein Western logic, which is witnessed by many influential works in...

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...

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...

In the paper, we try to find a new, intuitive solution to the Fitch paradox. We claim that traditional expression of Knowability Principle is based on erroneous understand-ing of knowability as de dicto modality. Instead, we propose to understand knowability as de re modality. In the paper we present the minimal logic of knowability in which Knowab...

In the article we present an extension of the minimal, normal positional logic, i.e., the logic with realization operator MR. Positional logic is a philosophical logic that makes it possible to relate sentences to contexts that can be understood in many ways. We enrich the basic language of minimal positional logic with additional expressions built...

This text has a programmatic and introductory character. In the paper, we outline a fine-grained semantics for intensional logics. The fundamental idea of the semantics is that the logical value of a given complex proposition is the result of two things: a valuation of propositional variables supplemented with a valuation of relation between the ma...

This talk is programmatic and introductory. We try to answer the questions of what the relating semantics is and of what relating logic is. We outline a fine-grained semantics for different kinds of logics. The fundamental idea of the semantics is that the logical value of a given complex proposition is the result of two things: a valuation of prop...

Relating logics are examples of non-classical logics that make it possible to seriously consider various non-logical relationships that occur between sentences. The main idea behind such logics is that logical values is not the only thing that matters when we consider truth conditions for formulas built by propositional connectives. What should be...

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 f...

In this paper, we indicate how Jan Woleński's non-linguistic concept of the norm allows us to clarify the deontic relationship between sentences and the given normative system. A relationship of this kind constitutes a component of the metalogic of relating deontic logic, which subjects the logical value of the deontic sentence to the logical value...

The aim of this paper is to show how to simply define paraconsistent tableaus by liberalization of construction of complete tableaus. The presented notions allow us to list all tableau inconsistencies that appear in a complete tableau. Then we can easily choose these inconsistencies that are effects of interactions between premises and a conclusion...

The book aims to formalise tableau methods for the logics of propositions and names. The methods described are based on Set Theory. The tableau rule was reduced to an ordered n-tuple of sets of expressions where the first element is a set of premises, and the following elemnts are its supersets.

In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic...

Theories of modal notions belong to subjects of permanent study for logicians as well as all philosophers. We describe some fundamental ideas concerning kinds of modal expressions. Then we deliver a concise introduction to basic concepts of modal logic with connectives M of possibility and L of necessity. We describe typical normal modal logic as s...

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.

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.

Most accounts, including leading textbooks, credit Arthur Nor-man Prior with the invention of temporal (tense logic). However, (i) JerzyŁoś delivered his version of temporal logic in 1947, several years beforePrior; (ii) Henrk Hiż’s review of Łoś’s system inJournal of Symbolic Logicwas published as early as 1951; (iii) there is evidence to the effe...

By a pure modal logic of names (PMLN) we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de re and which is an extension of Propositional Logic. For categorical sentences we use two interpretations: a “natural” one; and Johnson and Thomason’s in...

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w, where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the i...

In the paper we propose a new approach to formalization of cognitive logics. By cognitive logics we understand supraclassical, but non-trivial consequence operations, defined in a propositional language. We extend some paradigm of tableau methods, in which classical consequence Cn is defined, to stronger logics - monotonic, as well as non-monotonic...

The aim of this paper is to show how to simply define paraconsistent tableau systems by liberalization of construction of complete tableaus. The presented notions allow us to list all tableau inconsistencies that appear in a complete tableau. Then we can easily choose these inconsistencies that are effects of interactions between premises and a con...

The aim of the paper is to demonstrate and prove a tableau metatheorem for modal logics. While being effective tableau methods are usually presented in a rather intuitive way and our ambition was to expose the method as rigorously as possible. To this end all notions displayed in the sequel are couched in a set theoretical framework, for example: b...

In the paper we present tableau system ℱ for logic with relation imposed on formulae. The language for that logic consists of formulae built of the classical connectives and two new intensional connectives: related conjunction ▵ and related material conditional ↬. Models for ℱ are of the form 〈v,R〉 where v is a Boolean valuation and R is a binary r...

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom (P): ‘p Λ G p ⊃ P G p’. This formula was used by Prior...

This paper deals with the Aristotelian problem of sea-fight tomorrow, but it is analyzed from a Diodorean point of view. Precisely, we examine whether the lost argument of Diodor Cronus, called master argument, could be conducted within a frame of future open time. Since we do not know the argument itself, we follow the known reconstructions of mas...

In the article we present an application of some tableaux method presented by the author in [Log. Log. Philos. 16, No. 1, 85–101 (2007; Zbl 1140.03006)]. It is used to define a certain system of syllogistic. We consider only the basic system with Aristotelian sentences but without the assumption on non-emptiness. The presented approach can be effec...

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 ou...

The paper is devoted to a minimal system of R-operator (positional logic) with intensional interpretation of that operator. This is an intensional counterpart of system MR (minimal realization of R-operator, under the extensional interpretation).

The article presents a formalization of Anselm's so-called Ontological Arguments from Proslogion. The main idea of our research is to stay to the original text as close as is possible. We show, against some common opinions, that(i) the logic necessary for the formalization must be neither a purely sentential modal calculus, nor just non-modal first...

In the article "Podstawy analizy metodologicznej kanonow 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 Torun’. 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 fro...