Related papers: Natural Deduction as Higher-Order Resolution
Large Language Models (LLMs) have exhibited remarkable potential across a wide array of reasoning tasks, including logical reasoning. Although massive efforts have been made to empower the logical reasoning ability of LLMs via external…
Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
While large language models (LLMs) have demonstrated impressive performance in question-answering tasks, their performance is limited when the questions require knowledge that is not included in the model's training data and can only be…
Auditing is an increasingly important operation for computer programming, for example in security (e.g. to enable history-based access control) and to enable reproducibility and accountability (e.g. provenance in scientific programming).…
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent…
We introduced decomposable negation normal form (DNNF) recently as a tractable form of propositional theories, and provided a number of powerful logical operations that can be performed on it in polynomial time. We also presented an…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models. We introduce Latent Grammar Flow (LGF), a…
The motivation for this paper comes out of our experience with teaching natural deduction (ND) and with the way this formal system is implemented by the \textsc{Coq} proof assistant, namely by means of so-called tactics, which are…
Decomposition of text into atomic propositions is a flexible framework allowing for the closer inspection of input and output text. We use atomic decomposition of hypotheses in two natural language reasoning tasks, traditional NLI and…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Recent language models enable new opportunities for structured reasoning with text, such as the construction of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has…
In a recent paper, new theorems linking apparently unrelated mathematical objects (event structures from concurrency theory and full graphs arising in computational biology) were discovered by cross-site data mining on huge databases, and…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…