Symmetries in Modal Logics: A Coinductive Approach
نویسندگان
چکیده
We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models introduced in [4] and, hence, the results apply to a wide class of modal logics including, for example, hybrid logics. Our main result shows that the symmetries of a modal formula preserve entailment: if σ is a symmetry of φ then φ |= ψ if and only if φ |= σ(ψ).
منابع مشابه
Symmetries in Modal Logics
We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models introduced in [4] and, hence, the results apply to a wide class of modal logics including, for example, hybrid logics. Our main result shows that the symmetries of a modal formula preserve entailment: if σ is a symmetry of φ then φ |= ψ if and ...
متن کاملCoinductive models and normal forms for modal logics (or how we learned to stop worrying and love coinduction)
We present a coinductive definition of models for modal logics and show that it provides a homogeneous framework in which it is possible to include different modal languages ranging from classical modalities to operators from hybrid and memory logics. Moreover, results that had to be proved separately for each different language –but whose proofs were known to be mere routine– now can be proved...
متن کاملA Set-Theoretic Approach to Automated Deduction in Graded Modal Logics
In the paper, we consider the problem of supporting automated reasoning in a large class of knowledge representation formalisms, including terminological and epistemic logics, whose distinctive feature is the ability of representing and reasoning about finite quantities. Each member of this class can be represented using graded modalities, and thus the considered problem can be reduced to the p...
متن کاملA New Combination Procedure for the Word Problem That Generalizes Fusion Decidability Results in Modal Logics
Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics—which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equa...
متن کاملPractical Proof Methods for Combined Modal and Temporal Logics
For a number of years, temporal and modal logics have been applied outside pure logic in areas such as formal methods, theoretical computer science and artiicial intelligence. In our research we are particularly interested in the use of modal logics in the characterisation of complex components within software systems as intelligent or rational agents. This approach allows the system designer t...
متن کامل