103 documents found, page 1 of 11
Modality across different logics
Freire, Alfredo Roque; Martins, Manuel A.No abstract available.
Labeled fuzzy reactive graphs
Campos, Suene; Figueiredo, Daniel; Martins, Manuel A.; Santiago, RegivanThe topic of fuzzy and relation-changing structures has been progressively explored through the authors' previous work. This paper continues to expand the range of application for these models by introducing Labeled Fuzzy Reactive Graphs. This structure admits labels in regular edges, in order to permit to describe the action of different agents. For such structures, the operations of union, intersection and th...
Graded relation updates in modal logic
Fervari, Raul; Figueiredo, Daniel; Martins, Manuel A.This paper introduces a fuzzy approach to modal logics with graded relation updates. Specifically, we develop relation-changing modal logics where modalities modify the membership degree of a pair of elements in the accessibility relation. Our framework encompasses variants of local swap, sabotage, and bridge modalities. We motivate our approach via examples, and provide bisimulation notions for each logic, tog...
Characterization of lattice properties within modal extensions
Alfredo R. Freire; Martins, Manuel A.This paper investigates the extension of lattice-based logics into modal languages. We observe that such extensions admit multiple approaches, as the interpretation of the necessity operator is not uniquely determined by the underlying lattice structure. The most natural interpretation defines necessity as the meet of the truth values of a formula across all accessible worlds -- an approach we refer to as the \...
A function-set framework: general properties and applications to modal logic
Bayzid, Luke; Madeira, Alexandre; Martins, Manuel A.Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results between these representations can be non-trivial, as different frameworks are used for different contexts. We present a general structure based on set-theoretic concepts that...
Hybrid partial type theory
Manzano, María; Huertas, Antonia; Blackburn, Patrick; Martins, Manuel A.; Aranda, VíctorIn this article we define a logical system called Hybrid Partial Type Theory (HPTT). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of modal logic in which it is possible to name worlds and evaluate expressions with respec...
The institution of many-logics modal logic
Freire, Alfredo R.; Martins, Manuel A.; Madeira, AlexandreApproaching reconfigurable systems as structured transition systems, where the states are models in a given institution, is a methodological approach pursued in [17]. The versatility of this approach lies in the assumption that the logic used for configurations can be chosen based on the nature of the system configurations to be developed. Technically, this is supported by using parametric methods to build moda...
Reactive graphs in action
Tinoco, David; Madeira, Alexandre; Martins, Manuel A.; Proença, JoséReactive graphs are transition structures whereas edges become active and inactive during its evolution, that were introduced by Dov Gabbay from a mathematical’s perspective. This paper presents (https://fm-dcc.github.io/MARGe), a web-based tool to visualise and analyse reactive graphs enriched with labels. animates the operational semantics of reactive graphs and offers different graphical views to provide ins...
Relating Kleene algebras with pseudo uninorms
Bedregal, Benjamin; Santiago, Regivan; Madeira, Alexandre; Martins, Manuel A.This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect...
Relation-changing models meet paraconsistency
Costa, Diana; Figueiredo, Daniel; Martins, Manuel A.Switch graphs are graph-like structures characterized by embedding higher-level edges (edges that link to other edges) to describe reactive phenomena. When an edge of such structure is traversed, the accessibility relation of this graph can be changed by adding/removing edges. Relation-changing models have been used to represent phenomena in diverse fields (from Biology to Computer Science) and some modal langu...