Related papers: An Infinite Needle in a Finite Haystack: Finding I…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
The motivation of this study is to leverage recent breakthroughs in artificial intelligence research to unlock novel solutions to important scientific problems encountered in computational science. To address the human intelligence…
Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
Infinite-state systems such as distributed protocols are challenging to verify using interactive theorem provers or automatic verification tools. Of these techniques, deductive verification is highly expressive but requires the user to…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
The paper investigates from a proof-theoretic perspective various non-contractive logical systems circumventing logical and semantic paradoxes. Until recently, such systems only displayed additive quantifiers (Gri\v{s}in, Cantini). Systems…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…
Many computational problems can be modelled as the class of all finite structures $\mathbb A$ that satisfy a fixed first-order sentence $\phi$ hereditarily, i.e., we require that every (induced) substructure of $\mathbb A$ satisfies $\phi$.…
Quantified Conflict Driven Clause Leaning (QCDCL) is one of the main approaches to solving Quantified Boolean Formulas (QBF). Cube-learning is employed in this approach to ensure that true formulas can be verified. Dependency Schemes help…
Context: Safety is of paramount importance for cyber-physical systems in domains such as automotive, robotics, and avionics. Formal methods such as model checking are one way to ensure the safety of cyber-physical systems. However, adoption…