scholarly journals Hot: A concurrent automated theorem prover based on higher-order tableaux

1998 ◽  
pp. 245-261 ◽  
Author(s):  
Karsten Konrad
Keyword(s):  
Higher Order ◽  
Theorem Prover ◽  
Automated Theorem Prover

scholarly journals Leo-III Version 1.1 (System description)

10.29007/grmx ◽  
2018 ◽  
Author(s):  
Christoph Benzmüller ◽  
Alexander Steen ◽  
Max Wisniewski
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Higher Order Logic ◽  
System Description ◽  
Agent Based ◽  
First Order ◽  
Theorem Provers ◽  
Automated Theorem Prover ◽  
Ordering Constraints

Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers.Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use.

scholarly journals Embedding of Quantified Higher-Order Nominal Modal Logic into Classical Higher-Order Logic

10.29007/dzc2 ◽  
2018 ◽  
Author(s):  
Max Wisniewski ◽  
Alexander Steen
Keyword(s):  
Modal Logic ◽  
Higher Order ◽  
Order Logic ◽  
Tense Logic ◽  
Theorem Prover ◽  
Higher Order Logic ◽  
First Order ◽  
Automated Theorem Prover ◽  
Nominal Logic ◽  
The Moment

In this paper, we present an embedding of higher-order nominal modal logicinto classical higher-order logic, and study its automation. There exists no automated theorem prover for first-order or higher-order nominal logic at the moment, hence, this is the first automation for this kind of logic.In our work, we focus on nominal tense logic and have successfully proven some first theorems.

scholarly journals Going Polymorphic - TH1 Reasoning for Leo-III

10.29007/jgkw ◽  
2018 ◽  
Author(s):  
Alexander Steen ◽  
Max Wisniewski ◽  
Christoph Benzmüller
Keyword(s):  
Type Systems ◽  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Proof Assistants ◽  
Interactive Proof ◽  
Higher Order Logic ◽  
Theorem Provers ◽  
Reasoning System ◽  
Automated Theorem Prover

While interactive proof assistants for higher-order logic (HOL) commonly admit reasoning within rich type systems, current theorem provers for HOL are mainly based on simply typed lambda-calculi and therefore do not allow such flexibility. In this paper, we present modifications to the higher-order automated theorem prover Leo-III for turning it into a reasoning system for rank-1 polymorphic HOL.To that end, a polymorphic version of HOL and a suitable paramodulation-based calculus are sketched. The implementation is evaluated using a set of polymorphic TPTP THF problems.

scholarly journals CSE_E 1.0: An Integrated Automated Theorem Prover for First-Order Logic

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1142
Author(s):  
Feng Cao ◽  
Yang Xu ◽  
Jun Liu ◽  
Shuwei Chen ◽  
Xinran Ning
Keyword(s):  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Inference Mechanism ◽  
First Order ◽  
Proof Search ◽  
Interdisciplinary Field ◽  
Heuristic Strategies ◽  
Automated Theorem Prover ◽  
Hard Problems

First-order logic is an important part of mathematical logic, and automated theorem proving is an interdisciplinary field of mathematics and computer science. The paper presents an automated theorem prover for first-order logic, called C S E _ E 1.0, which is a combination of two provers contradiction separation extension (CSE) and E, where CSE is based on the recently-introduced multi-clause standard contradiction separation (S-CS) calculus for first-order logic and E is the well-known equational theorem prover for first-order logic based on superposition and rewriting. The motivation of the combined prover C S E _ E 1.0 is to (1) evaluate the capability, applicability and generality of C S E _ E , and (2) take advantage of novel multi-clause S-CS dynamic deduction of CSE and mature equality handling of E to solve more and harder problems. In contrast to other improvements of E, C S E _ E 1.0 optimizes E mainly from the inference mechanism aspect. The focus of the present work is given to the description of C S E _ E including its S-CS rule, heuristic strategies, and the S-CS dynamic deduction algorithm for implementation. In terms of combination, in order not to lose the capability of E and use C S E _ E to solve some hard problems which are unsolved by E, C S E _ E 1.0 schedules the running of the two provers in time. It runs plain E first, and if E does not find a proof, it runs plain CSE, then if it does not find a proof, some clauses inferred in the CSE run as lemmas are added to the original clause set and the combined clause set handed back to E for further proof search. C S E _ E 1.0 is evaluated through benchmarks, e.g., CASC-26 (2017) and CASC-J9 (2018) competition problems (FOFdivision). Experimental results show that C S E _ E 1.0 indeed enhances the performance of E to a certain extent.

scholarly journals Invariants and Robustness of BIP Models

10.29007/prxp ◽  
2018 ◽  
Author(s):  
Jan Olaf Blech ◽  
Thanh-Hung Nguyen ◽  
Michael Perin
Keyword(s):  
Embedded Systems ◽  
Higher Order ◽  
Theorem Prover ◽  
Important Goal ◽  
Invariant Generation ◽  
Execution Traces ◽  
Verification Tool ◽  
Verification Tools ◽  
Generation Mechanisms ◽  
Natural Way

In this paper we present on-going work addressing the problem of automatically generating realistic and guaranteed correct invariants. Since invariant generation mechanisms are error-prone, after the computation of invariants by a verification tool, we formally prove that the generated invariants are indeed invariants of the considered systems using a higher-order theorem prover and automated techniques. We regard invariants for BIP models. BIP (behavior, interaction, priority) is a language for specifying asynchronous component based systems. Proving that an invariant holds often requires an induction on possible system execution traces. For this reason, apart from generating invariants that precisely capture a system’s behavior, inductiveness of invariants is an important goal. We establish a notion of robust BIP models. These can be automatically constructed from our original non-robust BIP models and over-approximate their behavior. We motivate that invariants of robust BIP models capture the behavior of systems in a more natural way than invariants of corresponding non-robust BIP models. Robust BIP models take imprecision due to values delivered by sensors into account. Invariants of robust BIP models tend to be inductive and are also invariants of the original non-robust BIP model. Therefore they may be used by our verification tools and it is easy to show their correctness in a higher-order theorem prover. The presented work is developed to verify the results of a deadlock-checking tool for embedded systems after their computations. Therewith, we gain confidence in the provided analysis results.

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.

A prototype theorem-prover for a higher-order functional language

1985 ◽  
Vol 10 (4) ◽  
pp. 72-74
Author(s):  
Bob Boyer ◽  
Matt Kaufmann
Keyword(s):  
Higher Order ◽  
Theorem Prover ◽  
Functional Language

scholarly journals Engineering Software Correctness

2007 ◽  
Vol 17 (6) ◽  
pp. 675-686 ◽  
Author(s):  
REX PAGE
Keyword(s):  
Software Engineering ◽  
Functional Programming ◽  
Central Element ◽  
Theorem Prover ◽  
Good Design ◽  
Engineering Software ◽  
Automated Theorem Prover ◽  
New Perspective ◽  
Mechanical Logic ◽  
Software Correctness

AbstractDesign and quality are fundamental themes in engineering education. Functional programming builds software from small components, a central element of good design, and facilitates reasoning about correctness, an important aspect of quality. Software engineering courses that employ functional programming provide a platform for educating students in the design of quality software. This pearl describes experiments in the use of ACL2, a purely functional subset of Common Lisp with an embedded mechanical logic, to focus on design and correctness in software engineering courses. Students find the courses challenging and interesting. A few acquire enough skill to use an automated theorem prover on the job without additional training. Many students, but not quite a majority, find enough success to suggest that additional experience would make them effective users of mechanized logic in commercial software development. Nearly all gain a new perspective on what it means for software to be correct and acquire a good understanding of functional programming.

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