scholarly journals Implementing Different Proof Calculi for First-order Modal Logics

10.29007/mclw ◽  
2018 ◽  
Author(s):  
Christoph Benzmüller ◽  
Jens Otten ◽  
Thomas Raths
Keyword(s):  
Theorem Proving ◽  
Comparative Evaluation ◽  
Automated Theorem Proving ◽  
Modal Logics ◽  
First Order

This extended abstract presents several new automated theorem proving systems for first-order modal logics and sketches their calculi and working principles. The abstract also summarizes the results of a recent comparative evaluation of these new provers.

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 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 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.

Proof Procedures for Logic Programming

1998 ◽  
Author(s):  
Donald W. Loveland ◽  
Gopalan Nadathur
Keyword(s):  
Logic Programming ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Proof Procedure ◽  
Sld Resolution ◽  
Work Done ◽  
Resolution Proof

A proof procedure is an algorithm (technically, a semi-decision procedure) which identifies a formula as valid (or unsatisfiable) when appropriate, and may not terminate when the formula is invalid (satisfiable). Since a proof procedure concerns a logic the procedure takes a special form, superimposing a search strategy on an inference calculus. We will consider a certain collection of proof procedures in the light of an inference calculus format that abstracts the concept of logic programming. This formulation allows us to look beyond SLD-resolution, the proof procedure that underlies Prolog, to generalizations and extensions that retain an essence of logic programming structure. The inference structure used in the formulation of the logic programming concept and first realization, Prolog, evolved from the work done in the subdiscipline called automated theorem proving. While many proof procedures have been developed within this subdiscipline, some of which appear in Volume 1 of this handbook, we will present a narrow selection, namely the proof procedures which are clearly ancestors of the first proof procedure associated with logic programming, SLD-resolution. Extensive treatment of proof procedures for automated theorem proving appear in Bibel [Bibel, 1982], Chang and Lee [Chang and Lee, 1973] and Loveland [Loveland, 1978]. Although the consideration of proof procedures for automated theorem proving began about 1958 we begin our overview with the introduction of the resolution proof procedure by Robinson in 1965. We then review the linear resolution procedures, model elimination and SL-resolution procedures. Our exclusion of other proof procedures from consideration here is due to our focus, not because other procedures are less important historically or for general use within automated or semi-automated theorem process. After a review of the general resolution proof procedure, we consider the linear refinement for resolution and then further restrict the procedure format to linear input resolution. Here we are no longer capable of treating full first-order logic, but have forced ourselves to address a smaller domain, in essence the renameable Horn clause formulas. By leaving the resolution format, indeed leaving traditional formula representation, we see there exists a linear input procedure for all of first-order logic.

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