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A constructor-based approach for positive/negative-conditional equational specifications
[chapter]
1993
Lecture Notes in Computer Science
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We present a constructor-based approach for assigning appropriate semantics to algebraic speci cations given by nite sets of positive/negative-conditional equations. ...
) the minimum of all models that do not identify more constructor ground terms than necessary. ...
Acknowledgement: We would like to thank Ulrich K uhler for many valuable discussions and detailed criticisms on earlier versions of this paper. ...
doi:10.1007/3-540-56393-8_15
fatcat:5ebvwgrgpngq3ksx5y4snpddbe
A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications
1994
Journal of symbolic computation
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We present a constructor-based approach for assigning appropriate semantics to such speci cations. ...
We study algebraic speci cations given by nite sets R of positive/negative-conditional equations (i. e. universallyquanti ed rst-orderimplicationswith a single equation in the succedent and a conjunction ...
, J urgen Avenhaus and Klaus Becker for fruitful discussions, and Klaus Madlener and R udiger Lunde for useful hints. ...
doi:10.1006/jsco.1994.1004
fatcat:icf2mgkryzgqnoxunmndaqv6ee
Syntactic Confluence Criteria for Positive/Negative-Conditional Term Rewriting Systems
[article]
2009
arXiv
pre-print
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Finally, the whole paper may also give a practically useful overview of the syntactical means for showing confluence of conditional term rewriting systems. ...
of our syntactical separation into constructor and non-constructor symbols, we are able to present criteria for level confluence that are not criteria for shallow confluence actually and also able to ...
A Constructor-Based Approach for Positive/Negative-Conditional Equational Specifications. J. Symbolic Computation (1994) 17, pp. 51-90, Academic Press (Elsevier). ...
arXiv:0902.3614v1
fatcat:fl3fyfruqjewhlbjby3iyskmoy
Conditional equational specifications of data types with partial operations for inductive theorem proving
[chapter]
1997
Lecture Notes in Computer Science
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The language requires constructors for designating data items and admits positive/negative conditional equations as axioms in speci cations. ...
We propose a speci cation language for the formalization of data types with partial or non-terminating operations as part of a rewrite-based framework for inductive theorem proving. ...
Admissibility Conditions So far we have placed no restrictions on the set of positive/negative conditional equations in a speci cation with constructors. ...
doi:10.1007/3-540-62950-5_60
fatcat:4phcrk53ynendnmrl2lkkiwhn4
Page 5980 of Mathematical Reviews Vol. , Issue 94j
[page]
1994
Mathematical Reviews
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Summary: “We present two approaches to defining the semantics
for positive/negative conditional rewrite systems. ...
{For the entire collection see MR 94b:68025.}
94j:68132 68Q42
Becker, Klaus (D-KSRL-I; Kaiserslautern)
Semantics for positive /negative conditional rewrite systems. ...
Page 1109 of Mathematical Reviews Vol. , Issue 96b
[page]
1996
Mathematical Reviews
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A positive/negative-conditional equational specification is a finite set of finitary basic sentences [M. Makkai and R. ...
Bunder (5-WLG; Wollongong)
96b:68124 68Q65 68Q42
Wirth, Claus-Peter (D-KSRL-C; Kaiserslautern);
Gramlich, Bernhard (D-KSRL-C; Kaiserslautern)
A constructor-based approach to positive /negative-conditional ...
Page 3475 of Mathematical Reviews Vol. , Issue 94f
[page]
1994
Mathematical Reviews
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, Generic induction proofs (175-197); Claus-Peter Wirth and Bernhard Gramlich, A constructor-based approach for positive/negative-conditional equational specifications (198-212); Klaus Becker, Semantics ...
for positive/negative conditional rewrite systems (213-225); Harald Ganzinger and Jiirgen Stuber, Inductive theorem proving by consistency for first-order clauses (226-241); Francois Bronsard and Uday ...
Page 419 of Mathematical Reviews Vol. , Issue 95a
[page]
1995
Mathematical Reviews
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Zantema, Termination of term rewriting: interpretation and type elimination (23-50); Claus-Peter Wirth and Bernhard Gramlich, A constructor-based approach to positive/negative-conditional equational specifications ...
Singh, A semantics for speech acts (47- 71); Nelson Correa, Attribute and unification grammar: a review and analysis of formalisms (73-105); John Nerbonne, A feature- based syntax/semantics interface ( ...
Automation of Mathematical Induction as part of the History of Logic
[article]
2014
arXiv
pre-print
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relation after addition of the new positive/negative-conditional equations for the f k , assuming any arbitrary model M of all (positive/negative-conditional) equations with free constructors to be given ...
Moreover, the typed (many-sorted) approach of the positive/negative-conditional equations allows the presentation of formulas in a form that is much easier to grasp for human readers than the corresponding ...
arXiv:1309.6226v5
fatcat:i7nzngq47zfd7its4kfynlfpti
Contents EATCS Bulletin number 61, February 1997
1997
Theoretical Computer Science
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Wirth: Positive/Negative-Conditional Equations: A Constructor-Based Framework for Specification and Inductive Theorem Proving 93
Reports on Conferences
Twelfth Annual Meeting of the British Colloquium ...
Padberg: Abstract Petri Nets: Uniform Approach and Rule-Based Refinement G. Taentzer: Parallel and Distributed Graph Transformation: P. ...
doi:10.1016/s0304-3975(97)84330-7
fatcat:crayjadturb5jee3g2heonaaay
Algorithms in Philosophy, Informatics and Logic. A Position Manifesto 2017
2017
IfColog journal of logics and their applications (FLAP)
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We give more examples: • Consider a representation of an agent (irrespective of the exact theory used). ...
Boyer, Alan Bundy, Catherine Goldstein, Bernhard Gramlich, Warren A. ...
Burstall, Robert A. Kowalski, Pat Hayes, Gordon Plotkin, J Strother Moore, Mike J. C. Gordon, Robert S. ...
dblp:journals/flap/GabbayS17
fatcat:wvtsqquk3vhm3ohgsxn6lzc22u
Shallow confluence of conditional term rewriting systems
2009
Journal of symbolic computation
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Recursion can be conveniently modeled with left-linear positive/ negative-conditional term rewriting systems, provided that nontermination, non-trivial critical overlaps, non-right-stability, nonnormality ...
For such systems we present novel sufficient criteria for shallow confluence and arrive at the first decidable confluence criterion admitting nontrivial critical overlaps. ...
It was a pleasure to be taught by these masters of the field. ...
doi:10.1016/j.jsc.2008.05.005
fatcat:zjp4ce43onbfxbt3sv5g5wndoq
Using induction and rewriting to verify and complete parameterized specifications
1996
Theoretical Computer Science
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In software engineering there is a growing demand for formal methods for the specification and validation of software systems. ...
The formal development of a system might give rise to many proof obligations. We must prove the completeness of the specification and the validity of some inductive properties. ...
Acknowledgements I am grateful to Michael Rusinowitch, Hrlrne Kirchner, Toby Walsh, Peter Padawitz and Jiirgen Avenhaus for many fruitful discussions. ...
doi:10.1016/s0304-3975(96)80708-0
fatcat:53ewk2m25jgvpkby6w2cbwwaim
The Automation of Proof by Mathematical Induction
[chapter]
2001
Handbook of Automated Reasoning
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Thus mathematical induction is a key enabling technology for the use of formal methods in information technology. ...
Mathematical induction is required for reasoning about objects or events containing repetition, e.g. computer programs with recursion or iteration, electronic circuits with feedback loops or parameterized ...
The axioms of such a specification spec = (sig, E, A) are positive/negative conditional equations, they define new operators on top of a fixed built-in algebra A. ...
doi:10.1016/b978-044450813-3/50015-1
fatcat:y2m3e2cjjfhf5nvs734xddyxqi
An Even Closer Integration of Linear Arithmetic into Inductive Theorem Proving
2006
Electronical Notes in Theoretical Computer Science
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Successful approaches e.g. in NQTHM or ACL2 suggest a close integration scheme which augments the decision procedures with lemmas about user-defined operators. ...
We propose an even closer integration providing feedback about the state of the decision procedure in terms of entailed formulas for three reasons: First, to provide detailed proof objects for proof checking ...
Wirth, and the anonymous referees for helpful comments on earlier drafts of this paper. ...
doi:10.1016/j.entcs.2005.11.020
fatcat:nq5mi6sdofabznxf2kk74qsdci
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