Modal nonmonotonic logics: ranges, characterization, computation
Journal of the ACM (JACM)
Fundamenta Informaticae - Special issue: logics for artificial intelligence
Fundamenta Informaticae - Special issue on modal logics in knowledge representation
Fundamenta Informaticae - Special issue on modal logics in knowledge representation
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
Many-Valued Non-Monotonic Modal Logics
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
Compact Propositional Gödel Logics
ISMVL '98 Proceedings of the The 28th International Symposium on Multiple-Valued Logic
Algebraic Study of Lattice-Valued Logic and Lattice-Valued Modal Logic
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
A Duality for Algebras of Lattice-Valued Modal Logic
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Dualities for Algebras of Fitting's Many-Valued Modal Logics
Fundamenta Informaticae - Logic, Language, Information and Computation
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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 this kind have been recently investigated from the canonicity, completeness and correspondence perspective. In this paper, we provide some results on the effect of adopting weak versions of the axioms D, T, 4, 5 and w5 in the family of many-valued modal nonmonotonic logics, à la McDermott and Doyle, introduced in [4] and further investigated in [7]. For many-valued modal languages built on finite chains, we extend the results of [7] by proving two quite general range theorems. We then hint on the relation between the modal non-monotonic logics obtained: we prove that there exist ranges which selectively pick out some of the expansions produced by the many-valued autoepistemic logics introduced in [4, 9], actually the ones with a confidence-bounded set of beliefs. However, an exact charactelization of the relation between the various ranges created by the weak many-valued modal axioms still remains to be explored.