2 citations · 3 across the 8 of their papers we have counts for
9 papers
How Far Does Los's Theorem Extend To Kripke-Joyal Semantics? Sufficient Conditions, Counterexamples, and a Conjecture
Marc Aiguier, Romain Pascual
Los's theorem, also known as the fundamental result of ultraproducts, states that the ultraproduct over a family of structures for the same language satisfies a first-order formula…
Ultraproducts in abstract categorical logic
Marc Aiguier, Isabelle Bloch, Romain Pascual
In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formul…
Morpho-logic from a Topos Perspective: Application to symbolic AI
Marc Aiguier, Isabelle Bloch, Salim Nibouche +1
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, math…
Abstract Mathematical morphology based on structuring element: Application to morpho-logic
Marc Aiguier, Isabelle Bloch, Ramon Pino-Pérez
A general definition of mathematical morphology has been defined within the algebraic framework of complete lattice theory. In this framework, dealing with deterministic and increa…
Explanatory relations in arbitrary logics based on satisfaction systems, cutting and retraction
Marc Aiguier, Jamal Atif, Isabelle Bloch +1
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems…
Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning
Marc Aiguier, Isabelle Bloch
Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphol…