HOT: A Concurrent Automated Theorem Prover Based on Higher-Order Tableaux

@inproceedings{Konrad1998HOTAC,
  title={HOT: A Concurrent Automated Theorem Prover Based on Higher-Order Tableaux},
  author={Karsten Konrad},
  booktitle={TPHOLs},
  year={1998}
}
  • K. Konrad
  • Published in TPHOLs 27 September 1998
  • Computer Science, Mathematics
Hot is an automated higher-order theorem prover based on HTE, an extensional higher-order tableaux calculus. The first part of this paper introduces an improved variant of the calculus which closely corresponds to the proof procedure implemented in Hot. The second part discusses Hot's design that can be characterized as a concurrent blackboard architecture. We show the usefulness of the implementation by including benchmark results for over one hundred solved problems from logic and set theory. 
Superposition with Lambdas
TLDR
A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and implemented in the Zipperposition prover and evaluated on TPTP and Isabelle benchmarks.
Higher-Order Automated Theorem Proving
TLDR
The methods and proofand model-theoretic tools needed for extending first-order automated theorem proving to higherorder logic are exemplified and the deductive power of the calculus HT is characterized by the semantics of functional Σ-models.
Parallelization of a Hyper-Linking–Based Theorem Prover
TLDR
This work describes the parallelization of a first-order logic theorem prover that is based on the hyper-linking proof procedure (HLPP), and four parallel schemes are developed for two types of sequential implementation of HLPP: list based and network based.
TPS: A hybrid automatic-interactive system for developing proofs
A taxonomy of parallel strategies for deduction
  • M. Bonacina
  • Computer Science
    Annals of Mathematics and Artificial Intelligence
  • 2004
TLDR
This paper presents a taxonomy of parallel theorem-proving methods based on the control of search, the granularity of parallelism and the nature of the method, and analyzes how the different approaches to parallelization affect theControl of search.
Lightweight Semantic Web Oriented Reasoning in Prolog: Tableaux Inference for Description Logics
TLDR
The traditional Tableaux algorithm for Description Logics, a refined version of the algorithm is developed and a concrete implementation in Prolog, tableaux.pl, is proposed and compared to other implementations, both in terms of design and performance.
RECHERCHE Higher – Order Colored Unification : A Linguistic Application
TLDR
It is argued that Higher-Order Colored Unification (HOCU) can help prevent over-generation and the linguistic, logical and computational aspects of an HOCU–based approach to semantic construction are described.
A multi-agent framework for distributed theorem proving
Model Generation for Natural-language Semantic Analysis
TLDR
A discussion of Bry and Torge's hyper-resolution tableaux calculus EP as an approach to model generation for natural-language semantic analysis and some potential applications of model generators and model generation theorem provers in the construction and analysis of natural- language semantics.
Classical Type Theory
  • Peter B. Andrews
  • Computer Science, Mathematics
    Handbook of Automated Reasoning
  • 2001

References

SHOWING 1-10 OF 28 REFERENCES
Higher-Order Automated Theorem Proving for Natural Language Semantics
This paper describes a tableau-based higher-order theorem prover HOT and an application to natural language semantics. In this application, HOT is used to prove equivalences using world knowledge
Higher-Order Tableaux
TLDR
This paper presents two free variable tableau calculi for higher-order logic that use higher- order unification as the key inference procedure and differs in the treatment of the substitutional properties of equivalences.
A mechanization of sorted higher-order logic based on the resolution principle
TLDR
This thesis develops a sorted higher-order logic SUM HOL suitable for automatic theorem proving applications, and develops two notions of set-theoretic semantics for SUM HOL, which generalize general SUM-models further to SUM-model structures, which allow full extensionality to fail.
A Calculus and a System Architecture for Extensional Higher-Order Resolution
The first part of this paper introduces an extension for a variant of Huet's higher-order resolution calculus [Hue72, Hue73] based upon classical type theory (Church's typed A-calculus [Chu40]) in
First-Order Logic and Automated Theorem Proving
  • M. Fitting
  • Computer Science
    Graduate Texts in Computer Science
  • 1996
TLDR
This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style and is intended for those interested in computer science and mathematics at the beginning graduate level.
Proofs in Higher-Order Logic
TLDR
This work resolves the open question of what is a sound definition of skolemization in higher-order logic but also provides a direct, syntactic proof of its correctness.
Completeness in the Theory of Types
TLDR
This proof demonstrates that each formula of the calculus is a formal theorem which becomes a true sentence under every one of a certain intended class of interpretations of the formal system.
A Formulation of the Simple Theory of Types
TLDR
A formulation of the simple theory oftypes which incorporates certain features of the calculus of λ-conversion into the theory of types and is offered as being of interest on this basis.
Higher{order Coloured Uniication: a Linguistic Application
TLDR
A generalization of higher-order coloured uniication where the set of admissible colours is generalized from atomic expressions to rst-order feature trees and the desirability of the added expressivity in a linguistic application is shown.
...
...