Progress in the Development of Automated Theorem Proving for Higher-Order Logic

2009 ◽  
pp. 116-130 ◽  
Author(s):  
Geoff Sutcliffe ◽  
Christoph Benzmüller ◽  
Chad E. Brown ◽  
Frank Theiss
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic

scholarly journals Tutorial on Reasoning in Expressive Non-Classical Logics with Isabelle/HOL

10.29007/4dsr ◽  
2018 ◽  
Author(s):  
Alexander Steen ◽  
Max Wisniewski ◽  
Christoph Benzmüller
Keyword(s):  
Artificial Intelligence ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Description Logics ◽  
Automated Analysis ◽  
Higher Order ◽  
Order Logic ◽  
Proof Assistant ◽  
Higher Order Logic ◽  
Multimodal Logics

Non-classical logics (such as modal logics, description logics, conditional logics, multi-valued logics, hybrid logics, etc.) have many applications in artificial intelligence. In this tutorial, we will demonstrate a generic approach to automate propositional and quantified variants of non-classical logics using theorem proving systems for classical higher-order logic. Our particular focus will be on quantified multimodal logics. We will present and discuss a semantical embedding of quantified multimodal logics into classical higher-order logic, which enables the encoding and automated analysis of non-trivial modal logic problems in the Isabelle/HOL proof assistant. Additionally, TPTP compliant automated theorem proving systems can be called from within Isabelle’s Sledgehammer tool for automating reasoning tasks. In the tutorial, we will apply this approach to exemplarily solve a prominent puzzle from the AI literature: the well-known wise men.

scholarly journals Formalization of Linear Space Theory in the Higher-Order Logic Proving System

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Jie Zhang ◽  
Danwen Mao ◽  
Yong Guan
Keyword(s):  
Linear Space ◽  
Theorem Proving ◽  
Predicate Logic ◽  
Higher Order ◽  
Order Logic ◽  
First Order Logic ◽  
Space Theory ◽  
Higher Order Logic ◽  
First Order ◽  
Important Approach

Theorem proving is an important approach in formal verification. Higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and stronger semantics. Higher-order logic is more expressive. This paper presents the formalization of the linear space theory in HOL4. A set of properties is characterized in HOL4. This result is used to build the underpinnings for the application of higher-order logic in a wider spectrum of engineering applications.

scholarly journals Toward the Formalization of Macroscopic Models of Traffic Flow Using Higher-Order-Logic Theorem Proving

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 27291-27307
Author(s):  
Adnan Rashid ◽  
Muhammad Umair ◽  
Osman Hasan ◽  
Mohamed H. Zaki
Keyword(s):  
Traffic Flow ◽  
Theorem Proving ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Macroscopic Models

Probabilistic Analysis Using Theorem Proving

2015 ◽  
pp. 21-28
Keyword(s):  
Model Checking ◽  
Theorem Proving ◽  
Probabilistic Analysis ◽  
Probabilistic Model ◽  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Probabilistic Model Checking ◽  
Higher Order Logic ◽  
Comprehensive Framework

In this chapter, the authors first provide the overall methodology for the theorem proving formal probabilistic analysis followed by a brief introduction to the HOL4 theorem prover. The main focus of this book is to provide a comprehensive framework for formal probabilistic analysis as an alternative to less accurate techniques like simulation and paper-and-pencil methods and to other less scalable techniques like probabilistic model checking. For this purpose, the HOL4 theorem prover, which is a widely used higher-order-logic theorem prover, is used. The main reasons for this choice include the availability of foundational probabilistic analysis formalizations in HOL4 along with a very comprehensive support for real and set theoretic reasoning.

Formal Reliability Analysis of Engineering Systems

2014 ◽  
pp. 224-238
Author(s):  
Naeem Abbasi ◽  
Osman Hasan ◽  
Sofiène Tahar
Keyword(s):  
Reliability Analysis ◽  
Computer Simulations ◽  
Theorem Proving ◽  
Random Variables ◽  
Higher Order ◽  
Order Logic ◽  
Single Stage ◽  
Engineering Systems ◽  
Higher Order Logic ◽  
Computationally Expensive

Reliability analysis of engineering systems has traditionally been done using computationally expensive computer simulations that cannot attain 100% accuracy due to their inherent limitations. The authors conduct a formal reliability analysis using higher-order-logic theorem proving, which is known to be sound, accurate, and exhaustive. For this purpose, they present the higher-order-logic formalization of independent multiple continuous random variables, their verified probabilistic properties, and generalized relations for commonly encountered reliability structures in engineering systems. To illustrate the usefulness of the approach, the authors present the formal reliability analysis of a single stage transmission of an automobile.

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