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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…
As the interest in Artificial Intelligence continues to grow it is becoming more and more important to investigate formalization and tools that allow us to exploit logic to reason about the world. In particular, given the increasing number…
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…
Large language models increasingly function as artificial reasoners: they evaluate arguments, assign credibility, and express confidence. Yet their belief-forming behavior is governed by implicit, uninspected epistemic policies. This paper…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
We address the problem of belief revision of logic programs, i.e., how to incorporate to a logic program P a new logic program Q. Based on the structure of SE interpretations, Delgrande et al. adapted the well-known AGM framework to logic…
Autonomous systems require the management of several model views to assure properties such as safety and security among others. A crucial issue in autonomous systems design assurance is the notion of emergent behavior; we cannot use their…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in…
Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
Belief revision of knowledge bases represented by a set of sentences in a given logic has been extensively studied but for specific logics, mainly propositional, and also recently Horn and description logics. Here, we propose to generalize…
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…
This position paper argues that AI-assisted software engineering requires explicit mechanisms for tracking the epistemic status and temporal validity of architectural decisions. LLM coding assistants generate decisions faster than teams can…