Basic proof theory
Logic in computer science: modelling and reasoning about systems
Logic in computer science: modelling and reasoning about systems
Modal logic
A Labelled Sequent System for Tense Logic Kt
AI '98 Selected papers from the 11th Australian Joint Conference on Artificial Intelligence on Advanced Topics in Artificial Intelligence
Mathematical Structures in Computer Science
Actions and resources in epistemic logic
Actions and resources in epistemic logic
Aximo: Automated Axiomatic Reasoning for Information Update
Electronic Notes in Theoretical Computer Science (ENTCS)
Learning in a changing world, an algebraic modal logical approach
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
A categorical outlook on relational modalities and simulations
Information and Computation
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We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and S5, such logics are useful, as shown in previous work by Baltag, Coecke and the first author, for encoding and reasoning about information and misinformation in multi-agent systems. For such a logic we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of ''nested'' or ''tree-sequent'' calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.