We introduce a family of modal expansions of Belnap-Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice a...

s of the Talks In the order in which the talks were given. Walter Carnielli – Non-deterministic Semantics 5 Matthias Baaz – Analytic Calculi for Many-valued Logics 5 Hiroakira Ono – Many-valued Logics as Logics without the Contraction Rule 6 Reiner Hähnle – Proof Theory of Many-valued Logic and Hardware Design 7 Gonzalo Escalada-Imaz – Determining the Truth Degree in Real Time Settings 7 Peter ...

In his well-known paper \How computer should think" ((Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Speciically, w...

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a “modus-ponens-like” rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication-fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set...

A novel many-valued decomposition within the framework of lossless Reconstructability Analysis is presented. In previous work, Modified Recontructability Analysis (MRA) was applied to Boolean functions, where it was shown that most Boolean functions not decomposable using conventional Reconstructability Analysis (CRA) are decomposable using MRA. Also, it was previously shown that whenever decom...

The talk will began remembering results on papers [22, 15, 16] where the authors model uncertainty measures as fuzzy modalities on a many-valued residuated logics. the basic idea is that uncertainty measures is not a truth degree but could be interpreted as a truth degree of the fuzzy sentence ”the probability of φ”. The main properties being that the language does not allow nested modalities a...

The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by Wójcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued sema...

The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by Wójcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued sema...