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In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
Traditional ontologies describe domain structure but cannot generate novel artifacts. Large language models generate fluently but produce outputs lacking structural validity, hallucinating mechanisms without components, goals without end…
Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
Recent findings in multi-agent deep learning systems point towards the emergence of compositional languages. These claims are often made without exact analysis or testing of the language. In this work, we analyze the emergent language…
Programming languages are engineered languages that allow to instruct a machine and share algorithmic information; they have a great influence on the society since they underlie almost every information technology artefact, and they are at…
Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…
Idiomatic expressions are an integral part of natural language and constantly being added to a language. Owing to their non-compositionality and their ability to take on a figurative or literal meaning depending on the sentential context,…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural…
Normative non-functional requirements specify constraints that a system must observe in order to avoid violations of social, legal, ethical, empathetic, and cultural norms. As these requirements are typically defined by non-technical system…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
Ontologies are a popular way of representing domain knowledge, in particular, knowledge in domains related to life sciences. (Semi-)automating the process of building an ontology has attracted researchers from different communities into a…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…
We investigate the expressive power of a Turing-complete logic based on game-theoretic semantics. By defining suitable fragments and variants of the logic, we obtain a range of natural characterizations for some fundamental families of…
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 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…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
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…