Stable Modal Logics
نویسندگان
چکیده
We develop the theory of stable modal logics, a class of modal logics introduced in [3]. We give several new characterizations of stable modal logics, and show that there are continuum many such. Since some basic modal systems such as K4 and S4 are not stable, for a modal logic L, we introduce the concept of an L-stable extension of L. We prove that there are continuum many S4-stable modal logics, and continuum many K4-stable modal logics between K4 and S4. We axiomatize K4-stable and S4-stable modal logics by means of stable canonical formulas of [3], and discuss the connection between S4-stable modal logics and stable superintuitionistic logics of [2]. We conclude the paper with examples of K4-stable modal logics, and compare K4-stable modal logics to subframe and splitting transitive modal logics.
منابع مشابه
Logics with Common Weak Completions
We introduce the notion of X-stable models parametrized by a given logic X. Such notion is based on a construction that we call weak completions: a set of atoms M is an X-stable model of a theory T if M is a model of T, in the sense of classical logic, and the weak completion of T (namely T [ : e M) can prove, in the sense given by logic X, every atom in the set M. We prove that, for normal log...
متن کاملOn the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief
Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent’s rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer...
متن کاملStable Canonical Rules
We introduce stable canonical rules and prove that each normal modal multi-conclusion consequence relation is axiomatizable by stable canonical rules. We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable canonical rules. We also define stable multi-conclusion consequence relations and stable logics a...
متن کاملOn the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief
Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent?s rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer...
متن کاملOn the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief
Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent?s rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer...
متن کامل