A Logical Framework for Graded Predicates

Decidability and Complexity of Some Finitely-valued Dynamic Logics

“…It is natural to model graded n-ary relations (and, as a special case, vague relations) as functions from n-tuples of individuals to some (linearly ordered) set of truth degrees. The usual approach is to take an algebra based on the real unit interval [0, 1]; see (Cintula, Noguera, and Smith 2017;Hájek 1998;Smith 2008). For instance, Tall(john) may evaluate to 0.9 if John is 180 cm tall and Tall(jack) may evaluate to 0.3 if Jack is 170 cm tall.…”

“…Such results are the main contribution of the present paper. 1 Graded concepts are "a matter of more-or-less" (Cintula, Noguera, and Smith 2017); e.g. consider the role :IsEasilyAcces-sibleFrom or the concept GoodRestaurant (restaurants are good to a degree, some being better than others; physical locations are easily accessible from one another to a degree, some being more easy to get to than others).…”

Back-and-forth systems for fuzzy first-order models

“…As underlying propositional basis for the first-order predicate formalism, we choose a well-established class of propositional fuzzy logics: residuated uninormbased logics (studied in [28]). Such class provides a reasonable framework with several advantages: (1) it contains most of the well-studied particular systems of fuzzy logic that can be found in the literature, (2) it includes weakening-free logics and, hence, it benefits from their modeling power for reasoning with graded predicates as argued in [10], and (3) it retains the properties of associativity and commutativity of the residuated conjunction which simplifies the language and the formulation of many results.…”

Fraisse classes of graded relational structures

“…Most of the well-studied particular systems of fuzzy logic that can be found in the literature can be given a semantics on these algebras (cf. [6]).…”

“…6 Let xA, My be a countable weighted graph (where A is also countable). Then the following are equivalent.…”