Related papers: CycleQ: An Efficient Basis for Cyclic Equational R…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Contemporary proof assistants such as Coq require that recursive functions be terminating and corecursive functions be productive to maintain logical consistency of their type theories, and some ensure these properties using syntactic…
Chain-of-Thought reasoning can enhance large language models, but it requires manually designed prompts to guide the model. Recently proposed CoT-decoding enables the model to generate CoT-style reasoning paths without prompts, but it is…
We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as 'proofs', known as a the soundness condition. This soundness…
We present a straightforward source-to-source transformation that introduces justifications for user-defined constraints into the CHR programming language. Then a scheme of two rules suffices to allow for logical retraction (deletion,…
Cirquent calculus is a new proof-theoretic and semantic approach introduced for the needs of computability logic by G.Japaridze, who also showed that, through cirquent calculus, one can capture, refine and generalize independence-friendly…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
Recently, inference-time reasoning strategies have further improved the accuracy of large language models (LLMs), but their effectiveness on smaller models remains unclear. Based on the observation that conventional approaches often fail to…
We introduce a method of verifying termination of logic programs with respect to concrete queries (instead of abstract query patterns). A necessary and sufficient condition is established and an algorithm for automatic verification is…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
We introduce a novel learning and planning framework that replaces traditional reward-based optimisation with constructive logical inference. In our model, actions, transitions, and goals are represented as logical propositions, and…
Quorum systems are a powerful mechanism for ensuring the consistency of replicated data. Production systems usually opt for majority quorums due to their simplicity and fault tolerance, but majority quorum systems provide poor throughput…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
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…
Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
Large language models (LLMs) have achieved strong performance on complex reasoning tasks using techniques such as chain-of-thought and self-consistency. However, ensemble-based approaches, especially self-consistency which relies on…
Reasoning is essential for closed-domain QA systems in which procedural correctness and policy compliance are critical. While large language models (LLMs) have shown strong performance on many reasoning tasks, recent work reveals that their…
We describe the design and implementation of a reasoning engine that facilitates the gamification of loop-invariant discovery. Our reasoning engine enables students, computational agents and regular software engineers with no formal methods…
In logic-based approaches to reasoning tasks such as Recognizing Textual Entailment (RTE), it is important for a system to have a large amount of knowledge data. However, there is a tradeoff between adding more knowledge data for improved…