7,719 research outputs found
A Note on the Completeness of Many-Valued Coalgebraic Modal Logic
In this paper, we investigate the many-valued version of coalgebraic modal
logic through predicate lifting approach. Coalgebras, understood as generic
transition systems, can serve as semantic structures for various kinds of modal
logics. A well-known result in coalgebraic modal logic is that its completeness
can be determined at the one-step level. We generalize the result to the
finitely many-valued case by using the canonical model construction method. We
prove the result for coalgebraic modal logics based on three different
many-valued algebraic structures, including the finitely-valued {\L}ukasiewicz
algebra, the commutative integral Full-Lambek algebra (FL-algebra)
expanded with canonical constants and Baaz Delta, and the FL-algebra
expanded with valuation operations.Comment: 17 pages, preprint for journal submissio
Non-deterministic Semantics in Polynomial Format
AbstractThe method for automatic theorem proving proposed in [Carnielli, W. A., Polynomial ring calculus for many-valued logics, Proceedings of the 35th International Symposium on Multiple-Valued Logic, IEEE Computer Society. Calgary, Canada (2005), 20–25], called Polynomial Ring Calculus, is an algebraic proof mechanism based on handling polynomials over finite fields. Although useful in general domains, as in first-order logic, certain non-truth-functional logics and even in modal logics (see [Agudelo, J. C., Carnielli, W. A., Polynomial Ring Calculus for Modal Logics: a new semantics and proof method for modalities, The Review of Symbolic Logic. 4 (2011), 150–170, URL: doi:10.1017/S1755020310000213]), the method is particularly apt for deterministic and non-deterministic many-valued logics, as shown here. The aim of the present paper is to show how the method can be extended to any finite-valued non-deterministic semantics, and also to explore the computational character of the method through the development of a software capable of translating provability in deterministic and non-deterministic finite-valued logical systems into operations on polynomial rings
Towards a Proof Theory of G\"odel Modal Logics
Analytic proof calculi are introduced for box and diamond fragments of basic
modal fuzzy logics that combine the Kripke semantics of modal logic K with the
many-valued semantics of G\"odel logic. The calculi are used to establish
completeness and complexity results for these fragments
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