Many-Valued Non-Monotonic Modal Logics
نویسنده
چکیده
Among non-monotonic systems of reasoning, non-monotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce non-monotonic modal logics based on many-valued logics, rather than on classical logic. This extends earlier work of ours on many-valued modal logics. Intended applications are to situations involving several reasoners, not just one as in the standard development.
منابع مشابه
Weaker Axioms, More Ranges
In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language is based on an underlying Heyting algebra which provides the space of truth values. The lattice of truth values is explicitly represented in the language by a set of special constants and this allows for forming weak, generalized, many-valued analogs of all classical modal axioms. Weak axioms of th...
متن کاملOn the Proof Theory of Natural Many - valuedLogicsArnon
We claim that Proof Systems for natural many-valued logics, whether nite-valued or innnite-valued should be similar in their structure to proof systems of any other natural logic: one should not be able to tell from the structures which are used in a proof system the intended semantics. It is also preferable that standard connectives will be used, with corresponding standard rules. We demonstra...
متن کاملReduction of Many-valued into Two-valued Modal Logics
In this paper we develop a 2-valued reduction of many-valued logics, into 2-valued multi-modal logics. Such an approach is based on the contextualization of many-valued logics with the introduction of higher-order Herbrand interpretation types, where we explicitly introduce the coexistence of a set of algebraic truth values of original many-valued logic, transformed as parameters (or possible w...
متن کاملModal twist-structures over residuated lattices
We introduce a class of algebras, called twist-structures, whose members are built as special squares of an arbitrary residuated lattice. We show how our construction relates to and encompasses results obtained by several authors on the algebraic semantics of non-classical logics. We define a logic that corresponds to our twist-structures and show how to expand it with modal operators, obtainin...
متن کاملRevision by Translation
In this paper, we show that it is possible to accomplish belief revision in any logic which is translatable to classical logic. We start with the example of the propositional modal logic K and show that a belief operation in K de ned in terms of K0s translation to classical logic veri es the AGM postulates. We also consider the case of non-classical logics by taking Belnap's four-valued logic [...
متن کامل