Related papers: Formal Concept Analysis and Resolution in Algebrai…
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of…
Traditional knowledge graphs are constrained by fixed ontologies that organize concepts within rigid hierarchical structures. The root cause lies in treating domains as implicit context rather than as explicit, reasoning-level components.…
It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only if the context contains an n-dimensional contra-nominal scale as subcontext. In this work, we investigate more closely the interplay between the…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
In this paper, we propose a fresh perspective on argumentation semantics, to view them as a relational database. It offers encapsulation of the underlying argumentation graph, and allows us to understand argumentation semantics under a…
In the field of Judgment Aggrgation, a domain, that is a subset of a Cartesian power of $\{0,1\}$, is considered to reflect abstract rationality restrictions on vectors of two-valued judgments on a number of issues. We are interested in the…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of disjunctive logic programming generalized to algebraic domains. This system allows reasoning with information which is hierarchically structured and forms a (suitable)…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Interpretability has become an essential topic for artificial intelligence in some high-risk domains such as healthcare, bank and security. For commonly-used tabular data, traditional methods trained end-to-end machine learning models with…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…