Problem
Research questions and friction points this paper is trying to address.
intuitionistic modal logic
decidability
decision procedure
IS4
IK4
A decision procedure for intuitionistic modal logic IS4 (and IK4)
🤖 AI Summary
本文解决了直觉主义模态逻辑IS4和IK4的可判定性问题，通过提供一种构造性的决策程序，利用循环规则来证明或反驳给定公式。
📝 Abstract
In this paper, we show that the two intuitionistic modal logics IS4 and IK4 are decidable. We provide a constructive decision procedure, that, given a formula, produces either a proof showing the formula to be valid or a finite countermodel falsifying the formula, thus also proving the finite model property for both logics. The main ingredient of our strategy is the introduction of (possibly unsound) loop rules, which encode repeating behaviour in proof search. This paper fixes a previous mistake in our LICS'23 contribution.
Innovation
Methods, ideas, or system contributions that make the work stand out.
constructive decision procedure
finite model property
loop rules
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