Related papers: Beyond NP: Quantifying over Answer Sets
This paper describes an approach to the methodology of answer set programming (ASP) that can facilitate the design of encodings that are easy to understand and provably correct. Under this approach, after appending a rule or a small group…
We develop an inductive proof-technique to generate imperative programs for pointer data structures from behavioural specifications expressed in the Answer Set Programming (ASP) formalism. ASP is a non-monotonic logic based formalism that…
The paper presents an enhancement of xASP, a system that generates explanation graphs for Answer Set Programming (ASP). Different from xASP, the new system, xASP2, supports different clingo constructs like the choice rules, the constraints,…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
By incorporating the methods of Answer Set Programming (ASP) and Markov Logic Networks (MLN), LPMLN becomes a powerful tool for non-monotonic, inconsistent and uncertain knowledge representation and reasoning. To facilitate the applications…
In this paper, we examine the use of Conformal Language Modelling (CLM) alongside Answer Set Programming (ASP) to enhance the performance of standard open-weight LLMs on complex multi-step reasoning tasks. Using the StepGame dataset, which…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
To appear in Theory and Practice of Logic Programming (TPLP) Bound Founded Answer Set Programming (BFASP) is an extension of Answer Set Programming (ASP) that extends stable model semantics to numeric variables. While the theory of BFASP is…
We propose Differentiable Satisfiability and Differentiable Answer Set Programming (Differentiable SAT/ASP) for multi-model optimization. Models (answer sets or satisfying truth assignments) are sampled using a novel SAT/ASP solving…
Answering realistic questions about biological systems and pathways similar to the ones used by text books to test understanding of students about biological systems is one of our long term research goals. Often these questions require…
Answer-Set Programming (ASP) is a powerful and expressive knowledge representation paradigm with a significant number of applications in logic-based AI. The traditional ground-and-solve approach, however, requires ASP programs to be…
In Answer Set Programming (ASP), the user can define declaratively a problem and solve it with efficient solvers; practical applications of ASP are countless and several constraint problems have been successfully solved with ASP. On the…
Answer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
Over the last decades the development of ASP has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting…
This technical report describes the usage, syntax, semantics and core algorithms of the probabilistic inductive logic programming framework PrASP. PrASP is a research software which integrates non-monotonic reasoning based on Answer Set…
Detecting sets of relevant patterns from a given dataset is an important challenge in data mining. The relevance of a pattern, also called utility in the literature, is a subjective measure and can be actually assessed from very different…
Payroll management is a critical business task that is subject to a large number of rules, which vary widely between companies, sectors, and countries. Moreover, the rules are often complex and change regularly. Therefore, payroll…
The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…
In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the…