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We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…
We consider the recommendations of the World Wide Web Consortium (W3C) about the Resource Description Framework (RDF) and the associated query language SPARQL. We propose a new formal framework based on category theory which provides clear…
We describe a method and tool called \textit{ContractCheck} that allows for the consistency analysis of legal contracts, in particular Sales Purchase Agreements (SPAs). The analysis relies on an encoding of the premises for the execution of…
Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…
Constraint Handling Rules (CHR) are a committed-choice declarative language which has been designed for writing constraint solvers. A CHR program consists of multi-headed guarded rules which allow one to rewrite constraints into simpler…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to disprove termination of transition systems, and we evaluate its…
Task-oriented dialogues must maintain consistency both within the dialogue itself, ensuring logical coherence across turns, and with the conversational domain, accurately reflecting external knowledge. We propose to conceptualize dialogue…
HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…
Language model outputs are not always reliable, thus prompting research into how to adapt model responses based on uncertainty. Common approaches include: \emph{abstention}, where models refrain from generating responses when uncertain; and…
The semantics of probabilistic languages has been extensively studied, but specification languages for their properties have received little attention. This paper introduces the probabilistic dynamic logic pDL, a specification logic for…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
Specialized lexicons are collections of words with associated constraints such as special definitions, specific roles, and intended target audiences. These constraints are necessary for content generation and documentation tasks (e.g.,…
Extracting formal knowledge (ontologies) from natural language is a challenge that can benefit from a (semi-) formal linguistic representation of texts, at the semantic level. We propose to achieve such a representation by implementing the…
The Web of Linked Data is composed of tons of RDF documents interlinked to each other forming a huge repository of distributed semantic data. Effectively querying this distributed data source is an important open problem in the Semantic Web…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…