Defined over sets of truth values V which are closed subsets of [0, 1] containing both 0 and 1, Gödel logics GV are prominent examples of many-valued logics. We investigate a first-order fragment of GV extended with ∆ that is powerful enough to formalize important properties of fuzzy rule-based systems. The satisfiability problem in this fragment is shown to be NP-complete for all GV , also in ...

In AI and other branches of Computer Science expert models are often studied and used. Here we examine experts which evaluate formulas of modal logic. An expert model consists of a set of experts and a domination relation which dictates how each expert’s opinion is dependent upon the opinions expressed by other experts. Such multiple-expert modal models were introduced and investigated by Fitti...

Bosbach states represent a way of probabilisticly evaluating the formulas from various (commutative or non-commutative) many-valued logics. They are defined on the algebras corresponding to these logics with values in [0, 1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0, 1], in this paper we introduce Bosbach sta...

In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calcu...

Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the on...

Paradefinite (‘beyond the definite’) logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for defining paradefinite logics, consisting of four-valued matrices, and study the better accepted logics that are induced by these matric...

In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstra...

We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. The...

Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they a...

Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modelling the dynamics of a game frame whose states may correspond to different game forms. The two classes of effectivity functions studied are the families of playable and truly playable effectivity fu...