相关论文: Intuitionistic Existential Graphs from a non tradi…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with respect to every intermediate logic that is complete with…

There exist initial segments of both the Dyment lattice and the Dyment-Muchnik lattice that yield Brouwer algebras modeling exactly the intuitionistic propositional calculus. For the Dyment-Muchnik lattice, this result is obtained by…

In a 1985 commentary to his collected works, Kolmogorov remarked that his 1932 paper "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic logic] will become a permanent part of a [standard] course of…

The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…

We present (1) a new model for Peirce's full continuum (Vargas 2012-2015), based on an iterated sheaf of real numbers over all ordinal numbers, (2) a new model for Peirce's existential graphs (Oostra 2010), based on a new geometrical symbol…

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…

This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…

Van der Holst and Pendavingh introduced a graph parameter $\sigma$, which coincides with the more famous Colin de Verdi\`{e}re graph parameter $\mu$ for small values. However, the definition of $\sigma$ is much more geometric/topological…

We propose a new method for generating explanations with AI and a tool to test its expressive power within a user interface. In order to bridge the gap between philosophy and human-computer interfaces, we show a new approach for the…

We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited…

Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL, 18:837-858, 2010). In this paper,…

As part of a broader family of logics, [1, 3] introduced two key logical systems: $\mathsf{iK_{d}}$, which encapsulates the basic logical structure of dynamic topological systems, and $\mathsf{iK_{d*}}$, which provides a well-behaved yet…

A graph class admits an implicit representation if, for every positive integer $n$, its $n$-vertex graphs have a $O(\log n)$-bit (adjacency) labeling scheme, i.e., their vertices can be labeled by binary strings of length $O(\log n)$ such…

We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…

In 1936, Stanislaw Ja\'skowski gave a construction of an interesting sequence of what he called "matrices", which we would today call "finite Heyting Algebras". He then gave a very brief sketch of a proof that if a propositional formula…

Based on an ordering with directed lines and using constructions instead of existential axioms, von Plato proposed a constructive axiomatization of the ordered affine geometry. There are 22 axioms for the ordered affine geometry, of which…

This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is…

We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two…

The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born…