Many-valued coalgebraic modal logic with a semi-primal algebra of truth-degrees

Scientific Conference (2022, September 07)

A chain of adjuntions between BA and the variety generated by a semi-primal bounded lattice expansion

Scientific Conference (2021, June 12)

Associative, idempotent, symmetric, and order-preserving operations on chains

in Order: A Journal on the Theory of Ordered Sets and its Applications (2020), 37(1), 45-58

We characterize the associative, idempotent, symmetric, and order-preserving operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilattice order. In ... [more ▼]

We characterize the associative, idempotent, symmetric, and order-preserving operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilattice order. In particular, we prove that the number of associative, idempotent, symmetric, and order-preserving operations on an n-element chain is the nth Catalan number. [less ▲]

Extending maps to profinite completions in finitely generated quasivarieties

in Beiträge zur Algebra und Geometrie (2020), 61(4), 627-647

We consider the problem of extending maps from algebras to their profinite completions in finitely generated quasivarieties. Our developments are based on the construction of the profinite completion of ... [more ▼]

We consider the problem of extending maps from algebras to their profinite completions in finitely generated quasivarieties. Our developments are based on the construction of the profinite completion of an algebra as its natural extension. We provide an extension which is a multi-map and we study its continuity properties, and the conditions under which it is a map. [less ▲]

Categories of coalgebras for modal extensions of Łukasiewicz logic

Scientific Conference (2018, August 27)

The category of complete and completely distributive Boolean algebras with complete operators is dual to the category of frames. We lift this duality to the category of complete and completely ... [more ▼]

The category of complete and completely distributive Boolean algebras with complete operators is dual to the category of frames. We lift this duality to the category of complete and completely distributive MV-algebras with complete operators. [less ▲]

On associative, idempotent, symmetric, and nondecreasing operations

Scientific Conference (2018, July 02)

see attached file

Clones of pivotally decomposable operations

Scientific Conference (2018, June)

We investigate the clones of operations that are pivotally decomposable.

Pivotal decomposition schemes inducing clones of operations

in Beitraege zur Algebra und Geometrie = Contributions to Algebra and Geometry (2018), 59(1), 25-40

We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of ... [more ▼]

We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of pivotally decomposable operations are clones, and show that under certain assumptions these conditions are also necessary. In the latter case, the pivotal operation together with the constant operations generate the corresponding clone. [less ▲]

Modal Extensions of Łukasiewicz Logic for Modeling Coalitional Power

in Journal of Logic and Computation (2017), 27(1), 129-154

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 modeling ... [more ▼]

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 modeling 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 functions, respectively. In this paper we generalize the concept of effectivity function beyond the yes/no truth scale. This enables us to describe the situations in which the coalitions assess their effectivity in degrees, based on functions over the outcomes taking values in a finite Łukasiewicz chain. Then we introduce two modal extensions of Łukasiewicz finite-valued logic together with many-valued neighborhood semantics in order to encode the properties of many-valued effectivity functions associated with game forms. As our main results we prove completeness theorems for the two newly introduced modal logics. [less ▲]

Generalized qualitative Sugeno integrals

in Information Sciences (2017), 415-416

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of ... [more ▼]

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of Sugeno integrals on totally ordered bounded chains, by extending the operation that combines the value of the capacity on each subset of criteria and the value of the utility function over elements of the subset. We show that the generalized concept of Sugeno integral splits into two functionals, one based on a general multiple-valued conjunction (we call integral) and one based on a general multiple-valued implication (we call cointegral). These fuzzy conjunction and implication connectives are related via a so-called semiduality property, involving an involutive negation. Sugeno integrals correspond to the case when the fuzzy conjunction is the minimum and the fuzzy implication is Kleene-Dienes implication, in which case integrals and cointegrals coincide. In this paper, we consider a very general class of fuzzy conjunction operations on a finite setting, that reduce to Boolean conjunctions on extreme values of the bounded chain, and are non-decreasing in each place, and the corresponding general class of implications (their semiduals). The merit of these new aggregation operators is to go beyond pure lattice polynomials, thus enhancing the expressive power of qualitative aggregation functions, especially as to the way an importance weight can affect a local rating of an object to be chosen. [less ▲]