Related papers: Logical Primes, Metavariables and Satisfiability
Stalnaker and Thomason famously proved that the conditional logic \textsf{C2} with first-order quantifiers is complete with respect to a selection function semantics. However, the selection functions used in this completeness result take…
Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…
Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
A multiset of literals, called a clause, is \emph{strongly satisfied} by an assignment if \emph{no} literal evaluates to false. Finding an assignment that maximises the number of strongly satisfied clauses is NP-hard. We present a simple…
We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the…
This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…
Evaluations with accurate ground-truth labels (AGTLs) have been widely employed to assess predictive models for artificial intelligence applications. However, in some specific fields, such as medical histopathology whole slide image…
The rapid growth of data in the recent years has led to the development of complex learning algorithms that are often used to make decisions in real world. While the positive impact of the algorithms has been tremendous, there is a need to…
This paper describes a semantics for pure Prolog programs with negation that provides meaning to metaprograms. Metaprograms are programs that construct and use data structures as programs. In Prolog a primary mataprogramming construct is…
Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in natural language. Recent works show that such models can also produce the reasoning steps (i.e., the…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
Verifying the correctness of a textual statement requires not only semantic reasoning about the meaning of words, but also symbolic reasoning about logical operations like count, superlative, aggregation, etc. In this work, we propose…