Abstract Propositional inquisitive logic is the limit of its n -bounded approximations. In the predicate setting, however, this does not hold anymore, as discovered by Ciardelli and Grilletti [11], who also found complete axiomatizations of n -bounded inquisitive logics $$\textsf{InqBQ}_{n}$$ InqBQ n , for every fixed n . We introduce cut-free labelled sequent calculi for these logics. We illustrate the intricacies of schematic validity in such systems by showing that the well-known Casari formula is atomically valid in (a weak sublogic of) predicate inquisitive logic $$\textsf{InqBQ}$$ InqBQ , fails to be schematically valid in it, and yet is schematically valid under the finite boundedness assumption. The derivations in our calculi, however, are guaranteed to be schematically valid whenever a single specific rule is not used.

Abstract This paper proposes an intuitionistic generalization of van Benthem and Liu’s dynamic logic of relation changers, where relation changers are dynamic operators that rewrite each agent’s accessibility relation. We employ Nishimura’s Kripke semantics for a constructive propositional dynamic logic to define the semantics of relation changers. Strong completeness results of Hilbert-style axiomatizations for constructive dynamic logic of relation changers are established by two types of rewriting strategies via recursion axioms: inside-out and outside-in strategies. To establish the semantic completeness by outside-in strategy, we propose the notion of composition of relation changers and an appropriately defined notion of length of a formula. Moreover, we reveal that recursion axioms have additional two faces: semantic and proof-theoretic ones. As for the semantic face, we introduce an alternative semantics for dynamic logic of relation changers to specify the semantic meaning of recursion axioms used in the inside-out strategy. This leads us to a semantic completeness proof of the axiomatization for the original semantics, which does not require a rewriting strategy based on recursion axioms. As for the proof-theoretic face, we transform each of recursion axioms required in the outside-in strategy into two (left and right) inference rules to provide a sequent calculus for dynamic logic of relation changers. Since the resulting sequent calculus is cut-free but semi-analytic, it still enjoys the Craig interpolation theorem by Maehara’s method.

Abstract Dealing with preferences is a ubiquitous part of our daily lives, and thus, preference forms an integral part of our daily decision-making processes. If we consider preferences among groups of agents, deliberation often leads to changes in preferences of an agent, influenced by the opinions of others, depending on how reliable these agents are according to the agent under consideration. Sometimes, it also leads to changes in the opposite direction, i.e. reliability over agents gets updated depending on their preferences. There are various formal studies of preference change based on reliability and/or trust, but not the other way around—this work contributes to the formal study of the latter aspect, i.e. on reliability change based on agent preferences. In process, some policies of preference change based on agent reliabilities are also discussed. We introduce a novel formal study of the relevant changes in agent reliabilities in decision-making scenarios, which is an integral part of artificial intelligence studies in the current day. A two-dimensional hybrid language is proposed to describe such processes, and axiomatizations and decidability are discussed.

The author email addresses were previously assigned to the incorrect authors in this paper. This error has now been corrected online https://doi.org/10.1093/logcom/exaa067.

Abstract The paper presents semantically complete Hilbert-style systems for some variants of common sense modal predicate logic proposed by van Benthem and further developed by Seligman. The paper also investigates frame definability in the logics and shows what axiom schema is canonical in the logics. In addition to these semantic investigations on the logics, the paper provides the sequent calculi for some of the logics which enjoy cut elimination theorem.

Abstract Dynamic epistemic logic is a logic that is aimed at formally expressing how a person’s knowledge changes. We provide a cut-free labelled sequent calculus ($\textbf{GDEL}$) on the background of existing studies of Hilbert-style axiomatization $\textbf{HDEL}$ of dynamic epistemic logic and labelled calculi for public announcement logic. We first show that the $cut$ rule is admissible in $\textbf{GDEL}$ and show that $\textbf{GDEL}$ is sound and complete for Kripke semantics. Moreover, we show that the basis of $\textbf{GDEL}$ is extended from modal logic K to other familiar modal logics including S5 with keeping the admissibility of cut, soundness and completeness.

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, both in comparison with coalgebraic hybrid logics and with existing first-order proposals for special classes of Set-coalgebras (apart from relational structures, also neighbourhood frames and topological spaces). Basic model-theoretic constructions and results, in particular ultraproducts, obtain for the two classes that allow completeness---and in some cases beyond that. Finally, we discuss a basic sequent system, for which we establish a syntactic cut-elimination result.

This article studies two ways of updating neighbourhood models: updating by taking the intersection of the neighbourhoods with the announced proposition, and updating by selecting all the neighbourhoods that can entail the announced proposition. For each of these two ways, we establish reduction axioms, some model-theoretic results and algebraic semantics for public announcement logic, and dynamic epistemic logic of product update. We also study various concepts of group knowledge, including general knowledge, common knowledge, and distributed knowledge over neighbourhood models.

We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and modal logic. In addition, we give novel labeled tableau calculi for PD, MDL, and EMDL. We prove soundness, completeness and termination for each of the labeled calculi.