Implementing Connection Calculi for First-order Modal Logics
Jens Otten
- Vol. 22, pp 18-32
TLDR
In this article, an automated theorem prover for first-order modal logic is presented for the constant, cumulative, and varying domain of the modal logics D, T, S4, and S5.Abstract:
This paper presents an implementation of an automated theorem prover for first-order modal logic that works for the constant, cumulative, and varying domain of the modal logics D, T, S4, and S5. It is based on the connection calculus for classical logic and uses prefixes representing world paths and a prefix unification algorithm to capture the restrictions given by the Kripke semantics of the standard modal logics. This permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. Details of the calculus, the implementation and performance results on the QMLTP problem library are presented.read more
Citations
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Book ChapterDOI
MleanCoP: A Connection Prover for First-Order Modal Logic
TL;DR: MleanCoP is a fully automated theorem prover for first-order modal logic that supports heterogeneous multimodal logics and outputs a compact prefixed connection proof.
Proceedings ArticleDOI
Implementing and evaluating provers for first-order modal logics
TL;DR: This paper presents several implementations of fully automated theorem provers for first-order modal logics based on different proof calculi, among them the standard sequent calculus, a prefixed tableau calculus, an embedding into simple type theory, an instance-based method, and a Prefixed connection calculus.
Book ChapterDOI
The QMLTP problem library for first-order modal logics
Thomas Raths,Jens Otten +1 more
TL;DR: The Quantified Modal Logic Theorem Proving library provides a platform for testing and evaluating automated theorem proving systems for first-order modal logics and a small number of problems for multi-modal logic are included as well.
Book ChapterDOI
HOL Based First-Order Modal Logic Provers
TL;DR: The FMLtoHOL tool enables the application of off-the-shelf HOL provers and model finders for reasoning within first-order modal logics and sequentially schedules various HOL reasoners.
Book ChapterDOI
Advances in Connection-Based Automated Theorem Proving
TL;DR: Calculi to automate theorem proving in classical and some important non-classical logics, namely first- order intuitionistic and first-order modal logics are presented, which permits a goal-oriented and, hence, a more efficient proof search.
References
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