## leanTAP: Lean Tableau-based Deduction (1995)

Venue: | Journal of Automated Reasoning |

Citations: | 78 - 11 self |

### BibTeX

@ARTICLE{Beckert95leantap:lean,

author = {Bernhard Beckert and Joachim Posegga},

title = {leanTAP: Lean Tableau-based Deduction},

journal = {Journal of Automated Reasoning},

year = {1995},

volume = {15},

pages = {339--358}

}

### Years of Citing Articles

### OpenURL

### Abstract

. "prove((E,F),A,B,C,D) :- !, prove(E,[F---A],B,C,D). prove((E;F),A,B,C,D) :- !, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) :- !, "+length(C,D), copyterm((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[G---C],D). prove(A,,[C---D],,) :- ((A= -(B); -(A)=B)) -? (unify(B,C); prove(A,[],D,,)). prove(A,[E---F],B,C,D) :- prove(E,F,[A---B],C,D)." implements a first-order theorem prover based on free-variable semantic tableaux. It is complete, sound, and efficient. 1 Introduction The Prolog program listed in the abstract implements a complete and sound theorem prover for first-order logic; it is based on free-variable semantic tableaux (Fitting, 1990). We call this lean deduction: the idea is to achieve maximal efficiency from minimal means. We will see that the above program is indeed very efficient---not although but because it is extremely short and compact. Our approach surely does not lead to a deduction system which is superior to highly sophisticated systems li...

### Citations

409 |
First-Order Logic and Automated Theorem Proving
- Fitting
- 2012
(Show Context)
Citation Context ...e, sound, and efficient. 1 Introduction The Prolog program listed in the abstract implements a complete and sound theorem prover for first-order logic; it is based on free-variable semantic tableaux (=-=Fitting, 1990-=-). We call this lean deduction: the idea is to achieve maximal efficiency from minimal means. We will see that the above program is indeed very efficient---not although but because it is extremely sho... |

151 |
The Craft of Prolog
- O’Keefe
- 1990
(Show Context)
Citation Context ...tableau-based theorem provers. Thorough the paper we assume familiarity with free-variable tableaux for classical first-order logic (see e.g. (Fitting, 1990)) and the basics of programming in Prolog (=-=O'Keefe, 1990-=-). All source code given in this paper is available upon request from the authors. 2 The Program The idea behind leanT A P is to exploit the power of Prolog's inference engine as much as possible; whi... |

128 |
SETHEO: A High-Performance Theorem Prover
- Letz, Schumann, et al.
- 1992
(Show Context)
Citation Context ... although but because it is extremely short and compact. Our approach surely does not lead to a deduction system which is superior to highly sophisticated systems like Otter (McCune, 1990) or Setheo (=-=Letz et al., 1992-=-); these are better on solving difficult problems. However, many applications do not require deduction which is as complex as the state of the art in automated theorem proving can handle. Furthermore,... |

112 | SATCHMO: A theorem prover implemented in Prolog - Manthey, Bry - 1988 |

98 |
Seventy-Five Problems for Testing Automatic Theorem Provers
- Pelletier
- 1986
(Show Context)
Citation Context ... literals: nnf(Lit,,Lit,1). 4 Performance Although (or better: because) the prover is so small, it shows striking performance. Table 1 shows experimental results for a subset of Pelletier's problems (=-=Pelletier, 1986-=-). We placed the negated theorem in front of the axioms and used the above program for computing negation normal form. No. Limit Branches Time VarLim closed tried msec 17 1 14 14 0 18 2 1 1 9 19 2 4 6... |

60 |
2.0 Users Guide
- McCune, OTTER
- 1990
(Show Context)
Citation Context ...deed very efficient---not although but because it is extremely short and compact. Our approach surely does not lead to a deduction system which is superior to highly sophisticated systems like Otter (=-=McCune, 1990-=-) or Setheo (Letz et al., 1992); these are better on solving difficult problems. However, many applications do not require deduction which is as complex as the state of the art in automated theorem pr... |

39 | A tableau-based theorem prover - Oppacher, Suen, et al. - 1988 |

18 |
Relative Complexities of First-Order Calculi
- Eder
- 1992
(Show Context)
Citation Context ... formula is represented by a Prolog term (e.g., (p(0),all(N,(-p(N);p(s(N))))) stands for p(0)(8n(:p(n)p(s(n))))). We use a single Prolog predicate to implement our prover: 2 Using a definitional CNF (=-=Eder, 1992-=-) helps at most partially: it avoids exponential growth of formulae for the price of introducing some redundancy into the proof search. Extending the scope of quantifiers to clause level, however, can... |

10 |
The tableau-based theorem prover 3 T A P for multiple-valued logics
- Beckert, Gerberding, et al.
- 1992
(Show Context)
Citation Context ...erstanding. Both implementations have been carried out in Prolog. Based on experiences with the THOT theorem prover, the development of the 3 T A P system started around 1990 at Karlsruhe University (=-=Beckert et al., 1992-=-); the project was funded by IBM Germany and carried out by Peter Schmitt and Reiner Hahnle. The 3 T A P prover was again written in Prolog and implemented a calculus for free-variable tableaux, both ... |

10 | A mechanical proof procedure and its realization in an electronic computer - Prawitz, Prawitz, et al. - 1991 |

7 |
Deduktion mit Shannongraphen fur Pradikatenlogik erster Stufe
- POSEGGA
- 1993
(Show Context)
Citation Context ...mes as long. If leanT A P can solve a problem, its performance is in fact comparable to compilation-based systems that search for proofs by generating Prolog programs and running them (Stickel, 1988; =-=Posegga, 1993-=-a; Posegga, 1993b). Schubert's Steamroller (Pelletier No. 47) cannot be solved; this is no surprise, since the problem is designed for forward chaining based on clauses. It can only be proven in table... |

6 |
The even more liberalized ffi -rule in free variable semantic tableaux
- Beckert, ahnle, et al.
- 1993
(Show Context)
Citation Context ...es to insert a Skolem-term containing all variables that appear free on a branch; this is correct, but too restrictive: it often delays closing of inconsistent branches. The current state of the art (=-=Beckert et al., 1993-=-) is less restrictive: It suffices to use a Skolemterm that is unique (up to variable renaming) to the existentially quantified formula; this term only holds the free variables occurring in the formul... |

4 |
The THOT theorem prover
- Schmitt
- 1987
(Show Context)
Citation Context ...legal reasoning (Schonfeld, 1985). It was based on free-variable semantic tableaux and used unification for closing branches. A few years later Peter Schmitt developed the THOT theorem prover at IBM (=-=Schmitt, 1987-=-); this was also an implementation of free-variable tableaux and part of a project aiming at natural language understanding. Both implementations have been carried out in Prolog. Based on experiences ... |

3 | Compiling proof search in semantic tableaux
- Posegga
- 1993
(Show Context)
Citation Context ...mes as long. If leanT A P can solve a problem, its performance is in fact comparable to compilation-based systems that search for proofs by generating Prolog programs and running them (Stickel, 1988; =-=Posegga, 1993-=-a; Posegga, 1993b). Schubert's Steamroller (Pelletier No. 47) cannot be solved; this is no surprise, since the problem is designed for forward chaining based on clauses. It can only be proven in table... |

2 | An Improved Method for Adding Equality to Free Variable Semantic Tableaux - ahnle, Reiner - 1992 |

2 | 3rd Workshop on Theorem Proving with Analytic Tableaux and Related Methods - Broda, D'Agostino, et al. - 1994 |

1 | 2nd Workshop on Theorem Proving with Analytic Tableaux and Related Methods. Tech. rept. 213. MaxPlanck -Institut fur Informatik - Basin, ofer, et al. - 1993 |

1 | Grundlagen der Mathematik II. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berucksichtigung der Anwendungsgebiete - Hilbert - 1939 |

1 | Cooperation of Decision Procedures in a Tableau-Based Theorem Prover. Revue d'Intelligence Artificielle - aufl, Thomas - 1990 |

1 |
A Prolog Technology Theorem Prover. Pages 752--753
- Stickel
- 1988
(Show Context)
Citation Context ...ore than ten times as long. If leanT A P can solve a problem, its performance is in fact comparable to compilation-based systems that search for proofs by generating Prolog programs and running them (=-=Stickel, 1988-=-; Posegga, 1993a; Posegga, 1993b). Schubert's Steamroller (Pelletier No. 47) cannot be solved; this is no surprise, since the problem is designed for forward chaining based on clauses. It can only be ... |