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Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow…
CoAlgebraic Logic Programming (CoALP) is a dialect of Logic Programming designed to bring a more precise compile-time and run-time analysis of termination and productivity for recursive and corecursive functions in Logic Programming. Its…
Chain-of-thought (CoT) prompting has been widely adopted to enhance the reasoning capabilities of large language models (LLMs). However, the effectiveness of CoT reasoning is inconsistent across tasks with different reasoning types. This…
The assessment of explainability in Legal Judgement Prediction (LJP) systems is of paramount importance in building trustworthy and transparent systems, particularly considering the reliance of these systems on factors that may lack legal…
Legal Judgment Prediction (LJP) predicts applicable law articles, charges, and penalty terms from case facts. Beyond accuracy, LJP calls for intrinsically interpretable and legally grounded reasoning that can reconcile statutory rules with…
Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionistic basis through single-succedent sequent calculi. We adapt…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…
The Circularity Principle was successfully applied for developing a coinductive proving technique, known as circular coinduction. In this paper, we show that the same principle can be used to develop an inductive proving technique. A main…
Pre-trained large language models (LLMs) have been demonstrated to possess intrinsic reasoning capabilities that can emerge naturally when expanding the response space. However, the neural representation mechanisms underlying these…
Partially Observable Markov Decision Processes (POMDPs) are a powerful framework for planning under uncertainty. They allow to model state uncertainty as a belief probability distribution. Approximate solvers based on Monte Carlo sampling…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming…
A major challenge in inductive logic programming (ILP) is learning large programs. We argue that a key limitation of existing systems is that they use entailment to guide the hypothesis search. This approach is limited because entailment is…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
The development of person search techniques has been greatly promoted in recent years for its superior practicality and challenging goals. Despite their significant progress, existing person search models still lack the ability to…
Formal reasoning about inductively defined relations and structures is widely recognized not only for its mathematical interest but also for its importance in computer science, and has applications in verifying properties of programs and…
We introduce a generic presentation of 'syntactic objects built by mixed induction and coinduction' encompassing all standard kinds of infinitary terms, as well as derivation trees in non-wellfounded proof systems. We then define a notion…
Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…