Mateusz Klonowski

We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion.

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 of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules.

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 short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly as in Andersonian-Kangerian reduction, which uses different intensional implications and constants.

In this paper, we present the history of and the research directions in relating logic. For this purpose we will describe Epstein's Programme, which postulates accounting for the content of sentences in logical research. We will focus on analysing the content relationship and Epstein's logics that are based on it, which are special cases of relating logic. Moreover, the set-assignment semantics will be discussed. Next, the Torunian Programme of Relating Semantics will be presented; this programme explores the various non-logical relationships in logical research, including those which are content-related. We will present a general description of relating logic and semantics as well as the most prominent issues regarding the Torunian Programme, including some of its special cases and the results achieved to date.

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 or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic logic with respect to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches.

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, 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.

Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009) proved that the normal logics K45 , KB4 (=KB5), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45. Furthermore, a modal logic is a normal extension of K45 (resp. KD45; KB4; S5) if and only if it is determined by a set consisting of finite simplified frames (resp. such frames with A≠∅; such frames with A=W or A=∅; such frames with A=W). Secondly, for all normal extensions of K45, KB4, KD45 and S5, in particular for extensions obtained by adding the so-called “verum” axiom, Segerberg’s formulas and/or their T-versions, we prove certain versions of Nagle’s Fact (J Symbol Log 46(2):319–328, 1981) (which concerned normal extensions of K5). Thirdly, we show that these extensions are determined by certain classes of finite simplified frames generated by finite subsets of the set N of natural numbers. In the case of extensions with Segerberg’s formulas and/or their T-versions these classes are generated by certain finite subsets of N.

Fantastyka naukowa (ang. science fiction, w skrócie - SF) jest często przedstawianajako gatunek literacki dobrze przystosowany do spekulacji filozoficznej. SF i filozofia dzielą zainteresowanie kwestią nieśmiertelności, a ich ujęcia tego tematu można zestawić i porównać. Proponujemy tutaj zarys taksonomii różnych modeli czy wizji nieśmiertelności oferowanych przez filozofów i autorów fantastyki naukowej. Po wskazaniu istotnych rozbieżności między tymi modelami przedstawiamy sugestię, że pewne problemy oraz wątpliwości wysuwane przez pisarzy SF i filozofów wynikają z pomieszania różnych modeli. Mamy nadzieję, że te porównania pokażą wstępnie, w jakim sensie można powiedzieć, że fantastyka naukowa funkcjonuje jako dyskurs filozoficzny.

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.

The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent... knows/beliefs that...’. The second one is to define tableau systemsfor such logics. Firstly, we present the minimal positional logic MR. Then, we change the notion of formulas and semantics in order to consider iterations of the operator of realization and “free” classical formulas. After that, we move on to weaker logics in order to avoid the well known problem of logical omniscience. At the same time, we keep the positional counterparts of modal axioms, and. For all of the considered logics we present sound and complete tableau systems.

Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets.

In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: D (Dependence Logic), DD (Dual Dependence Logic), Eq (Logic of Equality of Content), S (Symmetric Relatedness Logic) and R (Nonsymmetric Relatedness Logic) (cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos 30(4):579–629, 2021, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those logics were defined by Carnielli. However, his approach has some limitations, for example, it requires a proof of functional completeness and axiomatization. Notwithstanding the first two constraints, it does not include all Epstein logics, e.g., logic Eq. Unlike Carnielli’s approach, here we use set-assignment semantics to determine those logics. Since syntax and semantics of a given logic usually determine a minimal syntax and structure of a tableau system for the logic along with other properties, we propose a uniform tableau framework for the logics determined by set-assignment semantics. What distinguishes our tableau systems is that they combine the features of tableaux for propositional logics and syllogistic logics when the problem of content of propositions is analysed in tableau proofs. To denote the content of propositions in the proofs, we use generalised labels (see Jarmużek and Goré in Landscapes in Logic, College Publications, London, 2021).