Related papers: Eliminating Unfounded Set Checking for HEX-Program…
In this paper we propose an extension of Answer Set Programming (ASP), and in particular, of its most general logical counterpart, Quantified Equilibrium Logic (QEL), to deal with partial functions. Although the treatment of equality in QEL…
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in…
In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite…
State-of-the-art answer set programming (ASP) solvers rely on a program called a grounder to convert non-ground programs containing variables into variable-free, propositional programs. The size of this grounding depends heavily on the size…
Head-elementary-set-free programs were proposed in (Gebser et al. 2007) and shown to generalize over head-cycle-free programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the…
Programming Computable Functions (PCF) is a simplified programming language which provides the theoretical basis of modern functional programming languages. Answer set programming (ASP) is a programming paradigm focused on solving search…
Fact-checking real-world claims often requires collecting multiple pieces of evidence and applying complex multi-step reasoning. In this paper, we present Program-Guided Fact-Checking (ProgramFC), a novel fact-checking model that decomposes…
Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
Bounded model checking of pointer programs is a debugging technique for programs that manipulate dynamically allocated pointer structures on the heap. It is based on the following four observations. First, error conditions like dereference…
Over-approximating (OX) program logics, such as separation logic (SL), are used for verifying properties of heap-manipulating programs: all terminating behaviour is characterised, but established results and errors need not be reachable. OX…
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…
Can non-programmers annotate natural language utterances with complex programs that represent their meaning? We introduce APEL, a framework in which non-programmers select among candidate programs generated by a seed semantic parser (e.g.,…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
$\alpha$Check is a light-weight property-based testing tool built on top of $\alpha$Prolog, a logic programming language based on nominal logic. $\alpha$Prolog is particularly suited to the validation of the meta-theory of formal systems,…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not…
Answer Set Programming (ASP) is an expressive knowledge representation and reasoning framework. Due to its rather simple syntax paired with high-performance solvers, ASP is interesting for industrial applications. However, to err is human…
How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…