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

Abstract

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.

Applications of Relating Semantics

“…Any models that mix relations with possible worlds can be named modalized models [see Jarmużek and Malinowski, 2019b;Jarmużek and Klonowski, 2020;Jarmużek and Paoli, 2021]). During the 1st WRL, the following problems were identified as some of the most important for the understanding of RL:…”

“…In the paper [Jarmużek and Paoli, 2021] the term Relating Logic (henceforth, RL) is defined as a term describing logic of relating connectives  similarly as Modal Logic is a logic of modal operators. 1 In turn, the basic idea behind a relating connectives is that the logical value of a given complex proposition is the result of two things:…”

“…2 On the other hand, we can look at when the semantics for a given language is called relating semantics. A semantics for the language is a relating semantics [see Jarmużek and Paoli, 2021] iff at least for one connective c i the valuation of all complex propositions of the form c i (ϕ 1 , . .…”

“…Some interesting cases are described, for example, in[Jarmużek and Paoli, 2021;Jarmużek and Klonowski, 2021;Paoli, 2007;Ledda et al, 2019], mainly in the implicational fragment of the defined language.…”

Axiomatization of BLRI Determined by Limited Positive Relational Properties

“…The 1st Workshop On Relating Logic took place in September 25-26, 2020. More on the workshop, see[Jarmużek and Paoli, 2021] …”