Related papers: A Resolution Prover for Coalition Logic

We report on COOL-MC, a model checking tool for fixpoint logics that is parametric in the branching type of models (nondeterministic, game-based, probabilistic etc.) and in the next-step modalities used in formulae. The tool implements…

Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…

While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…

Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…

We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…

The emergence of Large Language Models (LLMs) has demonstrated promising progress in solving logical reasoning tasks effectively. Several recent approaches have proposed to change the role of the LLM from the reasoner into a translator…

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…

We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP…

This paper describes a quantum algorithm for proof search in sequent calculus of a subset of Linear Logic using the Grover Search Algorithm. We briefly overview the Grover Search Algorithm and Linear Logic, show the detailed steps of the…

Large language models (LLMs) demonstrate superior reasoning capabilities compared to small language models (SLMs), but incur substantially higher costs. We propose COllaborative REAsoner (COREA), a system that cascades an SLM with an LLM to…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System C. For propositional…

Use of knowledge-based planning tools can help alleviate the challenges of planning a complex operation by a coalition of diverse parties in an adversarial environment. We explore these challenges and potential contributions of…

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…

This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…

Coalition Logic is an important logic in logical research on strategic reasoning. In two recent papers, Li and Ju argued that generally, concurrent game models, models of Coalition Logic, have three too strong assumptions: seriality,…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…

We interpret Linear Logic Proof Nets in a term language based on Solos calculus. The system includes a synchronisation mechanism, obtained by a conservative extension of the logic, that enables to define non-deterministic behaviours and…

We present an approach to obtain formally verified implementations of classical Computational Logic algorithms. We choose the Why3 platform because it allows to implement functions in a style very close to the mathematical definitions, as…