Related papers: Logic Programming with Satisfiability
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that…
Prolog is a well-known declarative programming language commonly used in introductory courses on logic and reasoning. However, many students find Prolog challenging because it lacks the familiar debugging mechanisms found in imperative…
As real logic programmers normally use cut (!), an effective learning procedure for logic programs should be able to deal with it. Because the cut predicate has only a procedural meaning, clauses containing cut cannot be learned using an…
ECLAIR is a Prolog-based prototype system aiming to provide a functionally complete environment for the study, development and evaluation of programming language analysis and implementation tools. In this paper, we sketch the overall…
Logic locking is a hardware security technique to intellectual property (IP) against security threats in the IC supply chain, especially untrusted fabs. Such techniques incorporate additional locking circuitry within an IC that induces…
Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine…
Answer Set Programming (ASP) is a successful method for solving a range of real-world applications. Despite the availability of fast ASP solvers, computing answer sets demands a very large computational power, since the problem tackled is…
The goal of inductive logic programming (ILP) is to search for a logic program that generalises training examples and background knowledge. We introduce an ILP approach that identifies minimal unsatisfiable subprograms (MUSPs). We show that…
Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for…
Large Reasoning Models (LRMs) have revolutionized complex problem-solving, yet they exhibit a pervasive "overthinking", generating unnecessarily long reasoning chains. While current solutions improve token efficiency, they often sacrifice…
Nature-inspired computation is receiving increasing attention. Various Ising machine implementations have recently been proven to be effective in solving numerous combinatorial optimization problems including maximum cut, low density parity…
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension…
Due to the adoption of horizontal business models following the globalization of semiconductor manufacturing, the overproduction of integrated circuits (ICs) and the piracy of intellectual properties (IPs) can lead to significant damage to…
We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially…
We introduce FRAT, a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to DRAT, the FRAT format allows solvers to include more information in proofs to reduce the computational cost of subsequent…
Adding interaction to logic programming is an essential task. Expressive logics such as linear logic provide a theoretical basis for such a mechanism. Unfortunately, none of the existing linear logic languages can model interactions with…
Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning…