8,344 research outputs found
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
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
Evidence-Based Beliefs in Many-Valued Modal Logics
Rational agents, humans or otherwise, build their beliefs from evidence – a process which we call consolidation. But how should this process be carried out? In this thesis, we study a multi-agent logic of evidence and the question how agents should form beliefs in this logic. The main contributions of this thesis are twofold. First, we present and study a many-valued modal logic, and show how it can be suitable for modelling multi-agent scenarios where each agent has access to some evidence, which in turn can be processed into beliefs. This is a technical and practical contribution to many-valued modal logics. Second, we open new paths for research in the field of evidence logics: we show a new approach based on many-valued logics, we highlight the concept of consolidations and the importance of looking at their dynamic nature, and build a methodology based on rationality postulates to evaluate them
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