Fundamenta Informaticae - Special issue: logics for artificial intelligence
Reasoning about knowledge and probability
Journal of the ACM (JACM)
Reasoning about knowledge
Many-Valued Non-Monotonic Modal Logics
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
A fuzzy modal logic for belief functions
Fundamenta Informaticae
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Algebraic Study of Lattice-Valued Logic and Lattice-Valued Modal Logic
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
Journal of Logic and Computation
Dualities for Algebras of Fitting's Many-Valued Modal Logics
Fundamenta Informaticae - Logic, Language, Information and Computation
Hi-index | 0.00 |
We formalize reasoning about fuzzy belief and fuzzy common belief, especially incomparable beliefs, in multi-agent systems by using a logical system based on Fitting's many-valued modal logic, where incomparable beliefs mean beliefs whose degrees are not totally ordered. Completeness and decidability results for the logic of fuzzy belief and common belief are established while implicitly exploiting the duality-theoretic perspective on Fitting's logic that builds upon the author's previous work. A conceptually novel feature is that incomparable beliefs and qualitative fuzziness can be formalized in the developed system, whereas they cannot be formalized in previously proposed systems for reasoning about fuzzy belief. We believe that belief degrees can ultimately be reduced to truth degrees, and we call this "the reduction thesis about belief degrees", which is assumed in the present paper and motivates an axiom of our system. We finally argue that fuzzy reasoning sheds new light on old epistemic issues such as coordinated attack problem.