Close semantics is introduced, a new possible-world semantics for such weak modal logics, and soundness and strong completeness for a range of systems are established.
Abstract
Weak modal logics can be obtained by restricting the axioms and inference rules governing the modal operator. At the extreme, one may consider the least modal logic, in which no specifically modal axiom or inference rule is imposed. We introduce closure semantics, a new possible-world semantics for such weak modal logics, and establish soundness and strong completeness for a range of systems. We also give truth-preserving translations between closure models and other possible-world semantics, including neighborhood, FMT, and Kripke semantics.
Motivated by relevant epistemic logic, we extend Dunn's simple Kripke-style binary relational semantics for the semi-relevant logic RM to fit a modal extension of RM. It is shown that the modal axioms and rules that need to be added to RM to obtain a sound and complete axiomatisation of its modal extension give an axio...
New proofs of weak normalization for intuitionistic and classical propositional logics (with the full set of operators -- falsum, implication, conjunction and disjunction) are presented and a deterministic algorithm for weak normalization is presented.
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This paper proposes a calculus for Dynamic Epistemic Logic (DEL) based on dynamic hypersequents, a new framework for capturing the dynamics of epistemic models in a purely structural and natural way. We enrich dynamic hypersequents with agent indices and an event store, yielding a uniform representation of epistemic ev...
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