scholarly journals Understanding LEO-II’s proofs

10.29007/x9c9 ◽  
2018 ◽  
Author(s):  
Nik Sultana ◽  
Christoph Benzmüller
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Higher Order ◽  
Target Audience ◽  
Theorem Prover ◽  
First Order

The LEO and LEO-II provers have pioneered the integration of higher-order and first-order automated theorem proving. To date, the LEO-II system is, to our knowledge, the only automated higher-order theorem prover which is capable of generating joint higher-order–first-order proof objects in TPTP format. This paper discusses LEO-II’s proof objects. The target audience are practitioners with an interest in using LEO-II proofs within other systems.

scholarly journals Checking the quality of clinical guidelines using automated reasoning tools

2008 ◽  
Vol 8 (5-6) ◽  
pp. 611-641 ◽  
Author(s):  
ARJEN HOMMERSOM ◽  
PETER J. F. LUCAS ◽  
PATRICK VAN BOMMEL
Keyword(s):  
Theorem Proving ◽  
Clinical Guidelines ◽  
Automated Reasoning ◽  
Automated Theorem Proving ◽  
Interactive Theorem Proving ◽  
Theorem Prover ◽  
First Order ◽  
Medical Quality ◽  
Diabetes Mellitus 2

AbstractRequirements about the quality of clinical guidelines can be represented by schemata borrowed from the theory of abductive diagnosis, using temporal logic to model the time-oriented aspects expressed in a guideline. Previously, we have shown that these requirements can be verified using interactive theorem proving techniques. In this paper, we investigate how this approach can be mapped to the facilities of a resolution-based theorem prover,otterand a complementary program that searches for finite models of first-order statements,mace-2. It is shown that the reasoning required for checking the quality of a guideline can be mapped to such a fully automated theorem-proving facilities. The medical quality of an actual guideline concerning diabetes mellitus 2 is investigated in this way.

scholarly journals Higher-order theorem proving and its applications

2019 ◽  
Vol 61 (4) ◽  
pp. 187-191
Author(s):  
Alexander Steen
Keyword(s):  
Theorem Proving ◽  
Formal Analysis ◽  
Logical Consequence ◽  
Effective Means ◽  
Industrial Applications ◽  
Higher Order ◽  
Hardware Verification ◽  
Theorem Prover ◽  
Computer Assisted ◽  
Higher Order Logic

Abstract Automated theorem proving systems validate or refute whether a conjecture is a logical consequence of a given set of assumptions. Higher-order provers have been successfully applied in academic and industrial applications, such as planning, software and hardware verification, or knowledge-based systems. Recent studies moreover suggest that automation of higher-order logic, in particular, yields effective means for reasoning within expressive non-classical logics, enabling a whole new range of applications, including computer-assisted formal analysis of arguments in metaphysics. My work focuses on the theoretical foundations, effective implementation and practical application of higher-order theorem proving systems. This article briefly introduces higher-order reasoning in general and presents an overview of the design and implementation of the higher-order theorem prover Leo-III. In the second part, some example applications of Leo-III are discussed.

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 Problem Libraries for Non-Classical Logics

10.29007/mkdw ◽  
2018 ◽  
Author(s):  
Jens Otten ◽  
Thomas Raths
Keyword(s):  
Theorem Proving ◽  
General Problem ◽  
Crucial Role ◽  
Automated Theorem Proving ◽  
Modal Logics ◽  
First Order ◽  
Problem Library ◽  
Future Plans

Problem libraries for automated theorem proving (ATP) systems play a crucial role when developing, testing, benchmarking and evaluating ATP systems for classical and non-classical logics. We provide an overview of existing problem libraries for some important non-classical logics, namely first-order intuitionistic and first-order modal logics. We suggest future plans to extend these existing libraries and discuss ideas for a general problem library platform for non-classical logics.

scholarly journals On Recurrent Neural Network Based Theorem Prover For First Order Minimal Logic

2021 ◽  
Vol 27 (11) ◽  
pp. 1193-1202
Author(s):  
Ashot Baghdasaryan ◽  
Hovhannes Bolibekyan
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Network ◽  
Theorem Proving ◽  
Recurrent Neural Networks ◽  
Selection Problem ◽  
Theorem Prover ◽  
Minimal Logic ◽  
Free System ◽  
First Order

There are three main problems for theorem proving with a standard cut-free system for the first order minimal logic. The first problem is the possibility of looping. Secondly, it might generate proofs which are permutations of each other. Finally, during the proof some choice should be made to decide which rules to apply and where to use them. New systems with history mechanisms were introduced for solving the looping problems of automated theorem provers in the first order minimal logic. In order to solve the rule selection problem, recurrent neural networks are deployed and they are used to determine which formula from the context should be used on further steps. As a result, it yields to the reduction of time during theorem proving.

scholarly journals Making Higher-Order Superposition Work

2021 ◽  
pp. 415-432
Author(s):  
Petar Vukmirović ◽  
Alexander Bentkamp ◽  
Jasmin Blanchette ◽  
Simon Cruanes ◽  
Visa Nummelin ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Inference Rules ◽  
Higher Order Logic ◽  
First Order ◽  
New Challenges

AbstractSuperposition is among the most successful calculi for first-order logic. Its extension to higher-order logic introduces new challenges such as infinitely branching inference rules, new possibilities such as reasoning about formulas, and the need to curb the explosion of specific higher-order rules. We describe techniques that address these issues and extensively evaluate their implementation in the Zipperposition theorem prover. Largely thanks to their use, Zipperposition won the higher-order division of the CASC-J10 competition.

scholarly journals Different Proofs are Good Proofs

10.29007/kwk9 ◽  
2018 ◽  
Author(s):  
Geoff Sutcliffe ◽  
Cynthia Chang ◽  
Li Ding ◽  
Deborah McGuinness ◽  
Paulo Pinheiro da Silva
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Problem Library

In order to compare the quality of proofs, it is necessary to measure artifacts of the proofs, and evaluate the measurements to determine differences between the proofs. This paper discounts the approach of ranking measurements of proof artifacts, and takes the position that different proofs are good proofs. The position is based on proofs in the TSTP solution library, which are generated by Automated Theorem Proving (ATP) systems applied to first-order logic problems in the TPTP problem library.

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.

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