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Variants of First-Order Modal Logics

by unknown authors
"... Abstract. In this paper we study proof procedures for some variants of first order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect t ..."
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Abstract. In this paper we study proof procedures for some variants of first order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect

Variants of First-Order Modal Logics

by Marta Cialdea Mayer, Serenella Cerrito , 2000
"... . In this paper we study proof procedures for some variants of rst order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We dene both ground and free variable tableau methods, parametric with respect to the va ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds where they are meant to be interpreted. 1 Introduction First order modal logics constitute a

HOL Provers for First-order Modal Logics — Experiments∗

by unknown authors
"... Higher-order automated theorem provers have been employed to automate first-order modal logics. Extending previous work, an experiment has been carried out to evaluate their collaborative and individual performances. 1 ..."
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Higher-order automated theorem provers have been employed to automate first-order modal logics. Extending previous work, an experiment has been carried out to evaluate their collaborative and individual performances. 1

Implementing and Evaluating Provers for First-order Modal Logics

by Christoph Benzmüller, Jens Otten, Thomas Raths
"... Abstract. While there is a broad literature on the theory of firstorder modal logics, little is known about practical reasoning systems for them. This paper presents several implementations of fully automated theorem provers for first-order modal logics based on different proof calculi. Among these ..."
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Abstract. While there is a broad literature on the theory of firstorder modal logics, little is known about practical reasoning systems for them. This paper presents several implementations of fully automated theorem provers for first-order modal logics based on different proof calculi. Among

Repairing the Interpolation Theorem in First-Order Modal Logic

by Carlos Areces, Patrick Blackburn, Maarten Marx , 2001
"... Introduction. Hybrid logics are extensions of orthodox modal logics in which it is possible to name worlds (or states, or times, . . . ). Such extensions have proved interesting for a number of reasons. We often want to reason about what happens at particular states, times, or locations, and this is ..."
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. Previous work has examined the e ects of hybridizing propositional modal logics. But what happens when a first-order modal logic is hybridized? First-order modal logics are often badly behaved - does hybridization improve the situation? As far as interpolation is concerned, yes. As we shall see

Lecture Notes on First-Order Modal Logic 15-816: Modal Logic

by André Platzer , 2010
"... In this lecture, we will introduce first-order modal logic and start considering its relationship to classical first-order logic. 2 ..."
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In this lecture, we will introduce first-order modal logic and start considering its relationship to classical first-order logic. 2

Implementing Connection Calculi for First-order Modal Logics

by Jens Otten - 9th International Workshop on the Implementation of Logics, Merida/Venezuela , 2012
"... 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 ..."
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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

HOL based first-order modal logic provers

by Thomas Raths - Proceedings of the 19th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), volume 8312 of LNCS , 2013
"... Abstract. First-order modal logics (FMLs) can be modeled as natural fragments of classical higher-order logic (HOL). The FMLtoHOL tool ex-ploits this fact and it enables the application of off-the-shelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmf-syntax ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
Abstract. First-order modal logics (FMLs) can be modeled as natural fragments of classical higher-order logic (HOL). The FMLtoHOL tool ex-ploits this fact and it enables the application of off-the-shelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmf

The QMLTP Problem Library for First-order Modal Logics

by Thomas Raths, Jens Otten - The 6th International Joint Conference on Automated Reasoning (IJCAR , 2012
"... Abstract. The Quantified Modal Logic Theorem Proving (QMLTP) library pro-vides a platform for testing and evaluating automated theorem proving (ATP) sys-tems for first-order modal logics. The main purpose of the library is to stimulate the development of new modal ATP systems and to put their compar ..."
Abstract - Cited by 7 (5 self) - Add to MetaCart
Abstract. The Quantified Modal Logic Theorem Proving (QMLTP) library pro-vides a platform for testing and evaluating automated theorem proving (ATP) sys-tems for first-order modal logics. The main purpose of the library is to stimulate the development of new modal ATP systems and to put

Topological Completeness of First-Order Modal Logic

by Steve Awodey, Kohei Kishida
"... As McKinsey and Tarski [20] showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the “necessity ” operation is modeled by taking the interior of an arbitrary subset of a topo ..."
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topological space. This topological interpretation was recently extended in a natural way to arbitrary theories of full first-order logic by Awodey and Kishida [3], using topological sheaves to interpret domains of quantification. This paper proves the system of full first-order S4 modal logic
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