Related papers: Self Provers and $\Sigma_1$ Sentences
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
Reasoning over natural language is a challenging problem in NLP. In this work, we focus on proof generation: Given a hypothesis and a set of supporting facts, the model generates a proof tree indicating how to derive the hypothesis from…
We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Sigma_1 level of the…
Let $\mathcal{PL}({\sf T},{\sf T}')$ and $\mathcal{PL}_{\Sigma_1}({\sf T},{\sf T}')$ respectively indicates the provability logic and $\Sigma_1$-provability logic of ${\sf T}$ relative in ${\sf T}'$. In this paper we characterize the…
As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena…
We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal{M}$, or an axiomatization $S$ thereof, we find a modal…
This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for…
We present a logic for the reasoning about necessity and justifications which is independent from relational semantics. We choose the concept of justification -- coming from a class of "Justification Logics" (Artemov 2008, Fitting 2009) --…
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
We present a new method, the Subdivision Construction, for proving the finite model property (the fmp) for broad classes of modal logics and modal rule systems. The construction builds on the framework of stable canonical rules, and…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics…
Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…
LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic…
Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any L_F-sentence \varphi containing only bounded quantifiers, and any positive rational number \delta, decides either "\varphi…