Book Chapter10.1093/oso/9780198537465.003.0004
Higher Order Logic
Daniël Leivant
- 17 Mar 1994
- pp 229-322
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TL;DR: Higher order logic is a foundational subject with practical applications in Theoretical Computer Science. It is characterized by its expressive power and is increasingly recognized for its importance.
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Abstract: Abstract Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to briefly point to some areas of current and potential applications. The chapter falls into two parts. The first part, consisting of sections 1 through 4, is designed to bring forth the essential issues and facts of the topic. Section 1 is intended to motivate our interest in higher order logic, by presenting selected examples of the expressive power of second order logic, and contrasting them with the limitations of first order logic.
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Citations
Using Decision Procedures with a Higher-Order Logic
Natarajan Shankar
- 03 Sep 2001
TL;DR: It is argued that higher-order logic and its variants actually achieve a happy medium between expressiveness and automation, particularly when used as a front-end to a wide range of decision procedures and deductive procedures.
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Fresh Logic: proof-theory and semantics for FM and nominal techniques
TL;DR: Fresh Logic is introduced, a natural deduction style first-order logic extended with term-formers and quantifiers derived from the FM-sets model of names and binding in abstract syntax and a proof-normalisation procedure for the intuitionistic case and a semantics based on Kripke models in FM- sets for which it is sound and complete.
27
Combining Model Checking and Deduction
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- 01 Jan 2018
TL;DR: The logical foundations of the two approaches to automated verification are examined and their similarities, differences, and complementarities are explored.
19
Co-simulation and Verification of a Non-linear Control System for Cogging Torque Reduction in Brushless Motors
Cinzia Bernardeschi,Pierpaolo Dini,Andrea Domenici,Sergio Saponara +3 more
- 16 Sep 2019
TL;DR: In this article, the benefits of integrating co-simulation and formal verification in the standard design flow of a brushless power drive system for precision robotic applications are demonstrated. But the authors focus on fine tuning of the controller gain parameters, exploiting the results from the formal verification.
16
Inductive Definability and the Situation Calculus
Eugenia Ternovskaia
- 23 Sep 1996
TL;DR: This work shows that the induction principle on situations is implied by an inductive definition of the set of situations and obtains essentially the same form of successor state axioms as [Rei91] and demonstrates a method of applying inductive definitions for computing fixed point properties of GOLOG programs.
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