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During the last decade, entity embeddings have become ubiquitous in Artificial Intelligence. Such embeddings essentially serve as compact but semantically meaningful representations of the entities of interest. In most approaches, vectors…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
Answer Set Programming (ASP) is a declarative problem solving paradigm that can be used to encode a combinatorial problem as a logic program whose stable models correspond to the solutions of the considered problem. ASP has been widely…
The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
It is common for search and optimization problems to have alternative equivalent encodings in ASP. Typically none of them is uniformly better than others when evaluated on broad classes of problem instances. We claim that one can improve…
Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
Answer Set Programming (ASP) is a well-known declarative formalism in logic programming. Efficient implementations made it possible to apply ASP in many scenarios, ranging from deductive databases applications to the solution of hard…
Understanding and controlling the informational complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
Abductive reasoning - the search for plausible explanations - has long been central to human inquiry, from forensics to medicine and scientific discovery. Yet formal approaches in AI have largely reduced abduction to eliminative search:…
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
A fundamental question in systems biology is the construction and training to data of mathematical models. Logic formalisms have become very popular to model signaling networks because their simplicity allows us to model large systems…
Serial pattern mining consists in extracting the frequent sequential patterns from a unique sequence of itemsets. This paper explores the ability of a declarative language, such as Answer Set Programming (ASP), to solve this issue…
Nested answer set programming (NASP; Lifschitz et al., 1999) generalizes answer set programming (ASP) by admitting nested expressions in rule bodies and heads, and thus, NASP aims at exploiting program succinctness. Yet, although NASP…
Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way…
Answer set programming (ASP) is a paradigm for modeling knowledge intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler…