Related papers: Nonground Abductive Logic Programming with Probabi…
We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on…
We present dPASP, a novel declarative probabilistic logic programming framework for differentiable neuro-symbolic reasoning. The framework allows for the specification of discrete probabilistic models with neural predicates, logic…
Answer-set programming (ASP) paradigm is a way of using logic to solve search problems. Given a search problem, to solve it one designs a theory in the logic so that models of this theory represent problem solutions. To compute a solution…
We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized.…
In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…
Large language models (LLMs) are increasingly used for program verification, and yet little is known about \emph{how} they reason about program semantics during this process. In this work, we focus on abstract interpretation based-reasoning…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
We study abductive, causal, and non-causal conditionals in indicative and counterfactual formulations using probabilistic truth table tasks under incomplete probabilistic knowledge (N = 80). We frame the task as a probability-logical…
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…
Slicing is a program analysis technique originally developed for imperative languages. It facilitates understanding of data flow and debugging. This paper discusses slicing of Constraint Logic Programs. Constraint Logic Programming (CLP) is…
The growing range of applications of Machine Learning (ML) in a multitude of settings motivates the ability of computing small explanations for predictions made. Small explanations are generally accepted as easier for human decision makers…
Large language models (LLMs) have recently demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed…
While large language models (LLMs), such as GPT-3, appear to be robust and general, their reasoning ability is not at a level to compete with the best models trained for specific natural language reasoning problems. In this study, we…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Abductive reasoning starts from some observations and aims at finding the most plausible explanation for these observations. To perform abduction, humans often make use of temporal and causal inferences, and knowledge about how some…
In spite of the rapidly increasing number of applications of machine learning in various domains, a principled and systematic approach to the incorporation of domain knowledge in the engineering process is still lacking and ad hoc solutions…
We propose a novel approach for answering and explaining multiple-choice science questions by reasoning on grounding and abstract inference chains. This paper frames question answering as an abductive reasoning problem, constructing…