• Corpus ID: 215785909

On Reductions of Hintikka Sets for Higher-Order Logic

  title={On Reductions of Hintikka Sets for Higher-Order Logic},
  author={Alexander Steen and Christoph Benzm{\"u}ller},
Steen's (2018) Hintikka set properties for Church's type theory based on primitive equality are reduced to the Hintikka set properties of Benzmuller, Brown and Kohlhase (2004) which are based on the logical connectives negation, disjunction and universal quantification. 
1 Citations

Extensional Higher-Order Paramodulation in Leo-III

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice that supports reasoning in polymorphic first-order and higher-order logic, in many quantified normal modal logics, as well as in different deontic logics.



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.

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

  • A. Steen
  • Computer Science
    KI - Künstliche Intelligenz
  • 2019
In this dissertation, both the theoretical and the practical challenges of designing an effective higher-order reasoning system are studied and the resulting system, the automated theorem prover Leo-III, is one of the most effective and versatile systems, in terms of supported logical formalisms, to date.

Semantic Techniques for Cut-Elimination in Higher Order Logic.

This paper extends the saturated abstract consistency approach and obtains analogous model existence results without assuming saturation, and shows that saturation can be as hard to prove as cut elimination.

An introduction to mathematical logic and type theory - to truth through proof

This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

A formulation of the simple theory of types

  • A. Church
  • Mathematics
    Journal of Symbolic Logic
  • 1940
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.

Church’s Type Theory

An Introduction to Mathematical Logic and Type Theory. Applied Logic Series

  • 2002