Related papers: On Establishing Robust Consistency in Answer Set P…

In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…

Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

Large language models frequently produce mutually inconsistent answers when reasoning over multiple related queries. We study case-file logical consistency: maintaining a globally satisfiable belief state across interdependent queries. We…

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance.…

In a plethora of recent work, large language models (LLMs) demonstrated impressive reasoning ability, but many proposed downstream reasoning tasks only focus on final answers. Two fundamental questions persist: 1) how consistent is the…

Most existing retrieval-augmented language models (LMs) assume a naive dichotomy within a retrieved document set: query-relevance and irrelevance. Our work investigates a more challenging scenario in which even the "relevant" documents may…

We show how definite extended logic programs can be used for defining and reasoning with rough sets. Moreover, a rough-set-specific query language is presented and an answering algorithm is outlined. Thus, we not only show a possible…

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…

Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

We present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be…

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs and efficient solvers. To enable access to external information, HEX-programs extend programs with external atoms, which allow for a…

Retrieval Augmented Generation (RAG) is a commonly used approach for enhancing large language models (LLMs) with relevant and up-to-date information. However, the retrieved sources can often contain conflicting information and it remains…

Achieving fault-tolerance will require a strong relationship between the hardware and the protocols used. Different approaches will therefore naturally have tailored proof-of-principle experiments to benchmark progress. Nevertheless,…

This work examines the use of contradiction in natural language inference (NLI) for question answering (QA). Typically, NLI systems help answer questions by determining if a potential answer is \emph{entailed} (supported) by some background…

Answer Set Programming (ASP) is a widely used declarative programming paradigm that has shown great potential in solving complex computational problems. However, the inability to natively support non-integer arithmetic has been highlighted…

Although many machine learning methods, especially from the field of deep learning, have been instrumental in addressing challenges within robotic applications, we cannot take full advantage of such methods before these can provide…

We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux…