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The main goal of this paper is to provide a ground-analysis of two classical connectives that have so far been ignored in the literature, namely the exclusive disjunction, and the ternary disjunction. Such ground-analysis not only serves to extend the applicability of the logic of grounding but also leads to a generalization of Poggiolesi (2016)'s definition of the notion of complete and immediate grounding. [ABSTRACT FROM AUTHOR]

The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory. [ABSTRACT FROM AUTHOR]

I argue that a recent philosophical interpretation by Jc Beall of the middle value of Weak Kleene (three-valued) logic (known also as Bochvar's logic) as 'being off-topic' is untenable. My main claim is that "being off-topic" is a relation, not a property, and as such cannot serve as an interpretation of a truth-value. [ABSTRACT FROM AUTHOR]

The paper surveys several views of proof-theoretic semantics and classifies them in accordance to the choice of which of the rules of a meaning-conferring natural-deduction system determines the meaning of the defined expression. Then, in contrast to the traditional approach that regards the rules as determining meaning implicitly, the paper proposes an explicit definition of meaning in terms of rules, appealing to collections of canonical derivations. A certain claim about a conclusion from the non-eliminability of the rules that are not meaning conferring is refuted, and an alternative explanation of non-eliminability is proposed. [ABSTRACT FROM AUTHOR]

The paper proposes an extension of the definition of a canonical proof, central to proof-theoretic semantics, to a definition of a canonical derivation from open assumptions. The impact of the extension on the definition of (reified) proof-theoretic meaning of logical constants is discussed. The extended definition also sheds light on a puzzle regarding the definition of local-completeness of a natural-deduction proof-system, underlying its harmony. [ABSTRACT FROM AUTHOR]

The article examines a Bilateral proof-theory of Relevant Logic which is based on a bilateral natural-deduction proof system. It reificates the theoretically determined meaning of logical constant. It also evaluates the natural deduction presentation of the implications of intuitionistic propositional logic.

The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Frege’s Context Principle, by taking “contributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting attribution of semantic values is discussed. Elsewhere, the same method was used for defining proof-theoretic meaning of subsentential phrases in a fragment of natural language. Doing the same for (the simpler and clearer case of) logic sheds more light on the proposal. [ABSTRACT FROM AUTHOR]

This paper develops a version of Natural Logic – an inference system that works directly on natural language syntactic representations, with no intermediate translation to logical formulae. Following work by Sánchez, we develop a small fragment that computes semantic order relations between derivation trees in Categorial Grammar. The proposed system has the following new characteristics: (i) It uses orderings between derivation trees as purely syntactic units, derivable by a formal calculus. (ii) The system is extended for conjunctive phenomena like coordination and relative clauses. This allows a simple account of non-monotonic expressions that are reducible to conjunctions of monotonic ones. (iii) A decision procedure for provability is developed for a fragment of Natural Logic. [ABSTRACT FROM PUBLISHER]