Related papers: An ExpTime Upper Bound for $\mathcal{ALC}$ with In…
One of the few available complete methods for checking the satisfiability of sets of polynomial constraints over the reals is the cylindrical algebraic covering (CAlC) method. In this paper, we propose an extension for this method to…
Recently, the description logic LE-ALC was introduced for reasoning in the semantic environment of the enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of ABoxes in this logic. In this paper, we…
Software requirement analysis can certainly benefit from prevention and early detection of failures, in particular by some kind of automatic analysis. Formal methods offer means to represent and analyze requirements with rigorous tools,…
We introduce CPDL+, a family of expressive logics rooted in Propositional Dynamic Logic (PDL). In terms of expressive power, CPDL+ strictly contains PDL extended with intersection and converse (a.k.a. ICPDL) as well as Conjunctive Queries…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…
In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression,…
Termination properties of actual Prolog systems with constraints are fragile and difficult to analyse. The lack of the occurs-check, moded and overloaded arithmetical evaluation via is/2 and the occasional nontermination of finite domain…
The Abstraction and Reasoning Corpus (ARC) is a challenging benchmark, introduced to foster AI research towards human-level intelligence. It is a collection of unique tasks about generating colored grids, specified by a few examples only.…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
We study bisimulations for useful description logics. The simplest among the considered logics is $\mathcal{ALC}_{reg}$ (a variant of PDL). The others extend that logic with inverse roles, nominals, quantified number restrictions, the…
Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with…
We show that the vast majority of extensions of the description logic $\mathcal{EL}$ do not enjoy the Craig interpolation nor the projective Beth definability property. This is the case, for example, for $\mathcal{EL}$ with nominals,…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
Large Language Models (LLMs) are capable of transforming natural language domain descriptions into plausibly looking PDDL markup. However, ensuring that actions are consistent within domains still remains a challenging task. In this paper…
Recent developments in machine learning have introduced models that approach human performance at the cost of increased architectural complexity. Efforts to make the rationales behind the models' predictions transparent have inspired an…
We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the…
Large language models have shown unprecedented abilities in generating linguistically coherent and syntactically correct natural language output. However, they often return incorrect and inconsistent answers to input questions. Due to the…
Many satisfiability modulo theories solvers implement a variant of the DPLL(T ) framework which separates theory-specific reasoning from reasoning on the propositional abstraction of the formula. Such solvers conclude that a formula is…
Dynamics and uncertainty are essential features of real-life argumentation, and many recent studies have focused on integrating both aspects into Dung's well-known abstract Argumentation Frameworks (AFs). This paper proposes a combination…