Related papers: Logic Programming for Describing and Solving Plann…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic…
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
The logical semantics of normal logic programs has traditionally been based on the notions of Clark's completion and two-valued or three-valued canonical models, including supported, stable, regular, and well-founded models. Two-valued…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
We examine how well the state-of-the-art (SOTA) models used in legal reasoning support abductive reasoning tasks. Abductive reasoning is a form of logical inference in which a hypothesis is formulated from a set of observations, and that…
Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
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…
Environments for systematic construction of logic programs are needed in the academy as well as in the industry. Such environments should support well defined construction methods and should be able to be extended and interact with other…
Acquiring factual knowledge with Pretrained Language Models (PLMs) has attracted increasing attention, showing promising performance in many knowledge-intensive tasks. Their good performance has led the community to believe that the models…
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
The system PL permits the translation of abstract proofs of program correctness into programs in a variety of programming languages. A programming language satisfying certain axioms may be the target of such a translation. The system PL…
Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task…
In the past years, deep learning models have been successfully applied in several cognitive tasks. Originally inspired by neuroscience, these models are specific examples of differentiable programs. In this paper we define and motivate…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
The development of highly fluent large language models (LLMs) has prompted increased interest in assessing their reasoning and problem-solving capabilities. We investigate whether several LLMs can solve a classic type of deductive reasoning…
Declarative approaches to process modeling are regarded as well suited for highly volatile environments as they provide a high degree of flexibility. However, problems in understanding and maintaining declarative business process models…