• Corpus ID: 10904377

Automating Quantified Multimodal Logics in Simple Type Theory -- A Case Study

  title={Automating Quantified Multimodal Logics in Simple Type Theory -- A Case Study},
  author={Christoph Benzm{\"u}ller},
In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP infrastructure for classical higher-order logic. 

Tables from this paper

Progress in Automating Higher-Order Ontology Reasoning
The Sigma knowledge engineering environment and the Suggested Upper-Level Ontology (SUMO) with the higher-order theorem prover LEO-II is integrated and a translation from SUMO’s SUO-KIF representations into the new typed higher- order form representation language TPTP THF is reported on.
The THFTPTP Project --- An Infrastructure for Typed Higher-order Form Automated Theorem Proving Marie Curie International Incoming Fellowship Grant Agreement PIIF-GA-2008-219982 Project Report --- Implications
The completed THFTPTP project has developed an infrastructure that supports research and development of automated theorem proving in higher-order logic so that they can be used as effective components of academic and industrial processes.
GridTPT: a distributed platform for Theorem Prover Testing
GridTPT is presented, the distributed platform for testing the veriT SMT solver, its features are fairly standard, but it allows to easily distribute the task in a cluster.


Progress in the Development of Automated Theorem Proving for Higher-Order Logic
Practical progress that has been made towards the goal of TPTP support for higher-order ATP systems is described.
Automating Access Control Logics in Simple Type Theory with LEO-II (Techreport)
This paper describes a sound and complete embedding of different access control logics in simple type theory and shows that the off the shelf theorem prover LEO-II can be applied to automate reasoning in prominent access controlLogics.
THF0 - The Core of the TPTP Language for Higher-Order Logic
The core of the TPTP language for higher-order logic --- THF0, based on Church's simple type theory, is introduced, a syntactically conservative extension of the untyped first-order TPTP Language.
Multimodal and intuitionistic logics in simple type theory
We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give
Higher-order semantics and extensionality
A methodology of abstract consistency methods is developed by providing the necessary model existence theorems needed to analyze completeness of (machine-oriented) higher-order calculi with respect to these model classes.
Natural Deduction for First-Order Hybrid Logic
  • T. Braüner
  • Philosophy, Computer Science
    J. Log. Lang. Inf.
  • 2005
The natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories.
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
This presentation discusses Functional Programming in HOL, which aims to provide students with an understanding of the programming language through the lens of Haskell.
Interpolation for first order S5
  • M. Fitting
  • Philosophy, Mathematics
    Journal of Symbolic Logic
  • 2002
It is shown that a first order S5 interpolation theorem can be proved provided the logic is extended to contain propositional quantifiers, and the result is proved.
Normal Multimodal Logics: Automatic Deduction and Logic Programming Extension
The aim of the proposal is not only to extend logic languages in order to perform epistemic reasoning and reasoning about actions but especially to provide tools for software engineering (e.g. modularity and inheritance among classes) retaining a declarative interpretation of the programs.