Related papers: ASPeRiX, a First Order Forward Chaining Approach f…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
Answer Set Programming (ASP) with stable model semantics has proven highly effective for knowledge representation and reasoning. However, the minimality requirement of stable models can be restrictive for applications requiring exploration…
We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao's theorem together with constraints directly in vector spaces…
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…
Answer Set Programming (ASP) is a well-established paradigm of declarative programming that has been developed in the field of logic programming and nonmonotonic reasoning. Advances in ASP solving technology are customarily assessed in…
Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can be stated about optimal solutions if an objective function is…
For widespread deployment in domains characterized by partial observability, non-deterministic actions and unforeseen changes, robots need to adapt sensing, processing and interaction with humans to the tasks at hand. While robots typically…
Answer Set Programming (ASP) is one of the major declarative programming paradigms in the area of logic programming and non-monotonic reasoning. Despite that ASP features a simple syntax and an intuitive semantics, errors are common during…
Answer Set Programming (ASP) is a popular declarative programming language for solving hard combinatorial problems. Although ASP has gained widespread acceptance in academic and industrial contexts, there are certain user groups who may…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
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…
Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs,…
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…
Most controlled natural languages (CNLs) are processed with the help of a pipeline architecture that relies on different software components. We investigate in this paper in an experimental way how well answer set programming (ASP) is…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…