Results 1  10
of
20
INKA: The Next Generation
, 1996
"... . The INKA system is a firstorder theorem prover with induction based on the explicit induction paradigm. Since 1986 when a first version of the INKA system was developed there have been many improvements. In this description we will give a short overview of the current system state and its abiliti ..."
Abstract

Cited by 41 (9 self)
 Add to MetaCart
. The INKA system is a firstorder theorem prover with induction based on the explicit induction paradigm. Since 1986 when a first version of the INKA system was developed there have been many improvements. In this description we will give a short overview of the current system state and its abilities. 1 Introduction The original INKA system dates back to 1986 [2]. The current version of the INKA system which will be described below has been developed at DFKI GmbH 1 between 1991 and 1995. The INKA system is a firstorder theorem prover with induction based on the explicit induction paradigm. In contrast to Nqthm, the BoyerMoore prover, [3], the system is based on a full firstorder calculus, a special variant of an ordersorted resolution calculus with paramodulation, [7]. However, it is not specialized on inductive proofs but possesses a powerful predicatelogic proof component. INKA is designed to be used for practical applications of inductive theorem proving, for instance, in th...
System Description: inka 5.0  A Logic Voyager
, 1999
"... this paper are implemented and used for some example logics and sequent calculus proof search. The core inka is implemented in Allegro Common Lisp. The interface runs on distributed Oz, which is available for Unix and Windows. As a next step we intend to integrate a logic for algorithmic function an ..."
Abstract

Cited by 23 (11 self)
 Add to MetaCart
this paper are implemented and used for some example logics and sequent calculus proof search. The core inka is implemented in Allegro Common Lisp. The interface runs on distributed Oz, which is available for Unix and Windows. As a next step we intend to integrate a logic for algorithmic function and predicate definitions as well as the methods to prove their termination as tactics. Termination proofs can be inspected and already proven lemmata can be used during the construction of termination proofs, which are the main advantages wrt. the black box implementation of these methods in the old inka system [8]. References
Annotated Reasoning
 Annals of Mathematics and Artificial Intelligence (AMAI). Special Issue on Strategies in Automated Deduction
, 2000
"... Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given goal, prove its abstracted version and then use the information about the resulting abstract proof as an outline to construct the proof at the ground level. Dierent techniques to abstract from details have been studied in the literature. The problem is to nd out which details should be abstracted away. On one hand, if we abstract too much information then we often obtain abstract solutions that cannot be transferred to the ground level. Then, planning at the abstract level is even more dicult than planning at the ground level because the abstraction removes necessary control information, or we obtain only little information from the abstract proof how to guide the proof at the ground leve...
A Pragmatic Approach to Reuse in Tactical Theorem Proving
, 2001
"... In interactive theorem proving, tactics and tacticals have been introduced to automate proof search. In this scenario, user interaction traditionally is restricted to the mode in which the user decides which tactic to apply on the toplevel, without being able to interact with the tactic once it ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
In interactive theorem proving, tactics and tacticals have been introduced to automate proof search. In this scenario, user interaction traditionally is restricted to the mode in which the user decides which tactic to apply on the toplevel, without being able to interact with the tactic once it has begun running. We propose a technique to allow the implementation of derivational analogy in tactical theorem proving. Instead of replaying tactics including backtracked dead ends our framework makes choice points in tactics explicit and thus avoids dead ends when reusing tactics. Additionally users can override choices a tactic has made or add additional steps to a derivation without terminating the tactic. The technique depends on an ecient replay of tactic executions without repeating search that the original computation may have involved. 1
Managing Structural Information by HigherOrder Colored Unification
 JOURNAL OF AUTOMATED REASONING
, 1999
"... Coloring terms (rippling) is a technique developed for inductive theorem proving which uses syntactic dierences of terms to guide the proof search. Annotations (colors) to symbol occurrences in terms are used to maintain this information. This technique has several advantages, e.g. it is highly go ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
Coloring terms (rippling) is a technique developed for inductive theorem proving which uses syntactic dierences of terms to guide the proof search. Annotations (colors) to symbol occurrences in terms are used to maintain this information. This technique has several advantages, e.g. it is highly goal oriented and involves little search. In this paper we give a general formalization of coloring terms in a higherorder setting. We introduce a simplytyped calculus with color annotations and present appropriate algorithms for the general, pre and pattern unification problems. Our work is a formal basis to the implementation of rippling in a higherorder setting which is required e.g. in case of middleout reasoning. Another application is in the construction of natural language semantics, where the color annotations rule out linguistically invalid readings that are possible using standard higherorder unification.
VSE: Controlling the Complexity in Formal Software Developments
 In Proceedings of the International Workshop on Applied Formal Methods
, 1998
"... . We give an overview of the enhanced VSE system which is a tool to formally specify and verify systems. It provides means for structuring specifications and it supports the development process from the specification of a system to the code generation. Formal developments following this method a ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
. We give an overview of the enhanced VSE system which is a tool to formally specify and verify systems. It provides means for structuring specifications and it supports the development process from the specification of a system to the code generation. Formal developments following this method are stored and maintained in an administration system that guides the user and maintains a consistent state. An integrated deduction system provides proof support for the deduction problems arising during the development process. 1 Introduction The reliability of complex software systems is becoming increasingly important for technical systems. Malfunctioning of software systems caused by design flaws or faulty implementations may lead to loss or garbling of data, breach of security, danger to life and limb, and, in almost all cases severe economic losses. In order to allow for an industrial development of software according to the highest IT security criteria (ITSEC), the VSE tool [5] ...
VSE: Formal Methods Meet Industrial Needs
, 2000
"... The Verification Support Environment (VSE) is a tool to formally specify and verify complex systems. It provides means to structure specifications and supports the development process from the specification of a system to the automatic generation of code. Formal developments following the VSE method ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
The Verification Support Environment (VSE) is a tool to formally specify and verify complex systems. It provides means to structure specifications and supports the development process from the specification of a system to the automatic generation of code. Formal developments following the VSE method are stored and maintained in an administration system that guides the user and maintains a consistent state of the development. An integrated deduction system provides proof support for the deduction problems arising during the development process. We describe the application of VSE to an industrial case study and give an overview of the enhanced VSE system and the VSE methodology.
Using Rippling for Equational Reasoning
 In Proceedings 20th German Annual Conference on Artificial Intelligence KI96
, 1996
"... . This paper presents techniques to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
. This paper presents techniques to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for planning of proofs. Rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. Fachbeitrag. Keywords: Automated reasoning, Theorem Proving, Rippling 1 Introduction Heuristics for judging similarities between formulas and subsequently reducing differences have been applied to automated deduction since the 1950s, when Newell, Shaw, and Simon built their first "logic machine" [NSS63]. Since the later 60s, a similar theme of difference identification and reduction appears in the field of resolution theorem proving [Mor69], [Dig85], [BS88]. Partial unifica...
HigherOrder Automated Theorem Proving
, 1998
"... Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or :A = 2 F. 2. If A 2 F and if B is the bhnormal form of A, then B F 2 Ñ S 2 . 3. If ::A 2 F, then A F 2 Ñ S . 4. If AB2F, then F A 2 Ñ S or F B 2 Ñ S . 5. If :(AB) 2 F, then F :A :B2 Ñ S . 6. If P a A 2 F, then F AB 2 Ñ S for each closed formula B 2 wff a (S). 7. If :P a A 2 F, then F :(Aw a ) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 8. If :(A = a!b B) 2 F, then F :(Aw a = Bw) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 9. If :(A = o B) 2 F, then F[fA;:Bg 2 Ñ S or F[f:A;Bg 2 Ñ S . Here, we treat equality as an abbreviation for Leibniz definition. We call an abstract consistency class saturated, iff for all F 2 Ñ S and all...