Related papers: Using Tableau to Decide Description Logics with Fu…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
We describe a class calculus that is expressive enough to describe and improve its own learning process. It can design and debug programs that satisfy given input/output constraints, based on its ontology of previously learned programs. It…
Multimodal representation learning is gaining more and more interest within the deep learning community. While bilinear models provide an interesting framework to find subtle combination of modalities, their number of parameters grows…
In this paper we present two terminating tableau calculi for propositional Dummett logic obeying the subformula property. The ideas of our calculi rely on the linearly ordered Kripke semantics of Dummett logic. The first calculus works on…
Explanations are often promoted as tools for transparency, but they can also foster confirmation bias; users may assume reasoning is correct whenever outputs appear acceptable. We study this double-edged role of Chain-of-Thought (CoT)…
One of the main advantages of Prolog is its potential for the implicit exploitation of parallelism and, as a high-level language, Prolog is also often used as a means to explicitly control concurrent tasks. Tabling is a powerful…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…
In an open, constantly changing and collaborative environment like the forthcoming Semantic Web, it is reasonable to expect that knowledge sources will contain noise and inaccuracies. It is well known, as the logical foundation of the…
Chain-of-Thought (CoT) has unlocked advanced reasoning abilities of Large Language Models (LLMs) with intermediate steps, yet incurs prohibitive computational costs due to generation of extra tokens. Recent studies empirically show that…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…
We explore the relationships between Description Logics and Set Theory. The study is carried on using, on the set-theoretic side, a very rudimentary axiomatic set theory Omega, consisting of only four axioms characterizing binary union, set…
There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
In their recent paper (GandALF 2018), Goubault, Ledent, and Rajsbaum provided a formal epistemic model for distributed computing. Their logical model, as an alternative to the well-studied topological model, provides an attractive framework…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such…
Evaluating LLM agent trajectories is fundamentally task-specific: a code-debugging agent should be judged on Correctness and Error Handling, not on Fluency or Safety. Yet the dominant paradigm -- LLM-as-Judge with a fixed rubric -- applies…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…