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ASF+ --- eine ASF-aehnliche Spezifikationssprache [article]

Ruediger Lunde, Claus-Peter Wirth
2009 arXiv   pre-print
Da der Spezifikationssemantik ein konstruktorbasierter Ansatz zu Grunde liegt (vergleiche etwa [Wirth&Gramlich93] oder [Wirth&Gramlich94] ), wird zwischen constructors und non-constructors unterschieden  ...  Für die genaue Bedeutung der Makros @, case, if und else sei auf [Wirth&Lunde94] verwiesen.  ... 
arXiv:0902.2995v1 fatcat:2ap7zjn5gvb2zhdzeiypglwnq4

Writing Positive/Negative-Conditional Equations Conveniently [article]

Claus-Peter Wirth, Ruediger Lunde
2009 arXiv   pre-print
Introduction Introduction We present a macro-rule-construct for convenient specification with positive/negative-conditional equations as presented in Wirth & Gramlich (1993) .  ... 
arXiv:0902.2975v1 fatcat:uxwmamiquzefboonm35z7qlr6i

Herbrand's Fundamental Theorem - an encyclopedia article [article]

Claus-Peter Wirth
2015 arXiv   pre-print
It was clearly outlined by Jean van Heijenoort, but first sketched in publication in [ Wirth &al., 2009 ] , and first published with an explicit presentation in [ Wirth, 2012 ] .  ...  Conclusion In this article we have delivered what we consider the very essentials that any logician should know on Herbrand's Fundamental Theorem, and we suggest [ Wirth, 2014 ] and [ Wirth &al., 2014  ... 
arXiv:1503.01412v1 fatcat:jgg3fsy3czev3f4nixnhvk3qmu

An Algebraic Dexter-Based Hypertext Reference Model [article]

Volker Mattick, Claus-Peter Wirth
2009 arXiv   pre-print
We present the first formal algebraic specification of a hypertext reference model. It is based on the well-known Dexter Hypertext Reference Model and includes modifications with respect to the development of hypertext since the WWW came up. Our hypertext model was developed as a product model with the aim to automatically support the design process and is extended to a model of hypertext-systems in order to be able to describe the state transitions in this process. While the specification
more » ... specification should be easy to read for non-experts in algebraic specification, it guarantees a unique understanding and enables a close connection to logic-based development and verification.
arXiv:0902.3648v1 fatcat:iq5n4mqxqrczdpxduaedzdggau

Syntactic Confluence Criteria for Positive/Negative-Conditional Term Rewriting Systems [article]

Claus-Peter Wirth
2009 arXiv   pre-print
Claus-Peter Wirth, Bernhard Gramlich (1994b). On Notions of Inductive Validity for First-Order Equational Clauses. 12 th CADE 1994, LNAI 814, pp. 162-176, Springer.  ...  Revised and extended version is Wirth & Gramlich (1994a). Claus-Peter Wirth, Bernhard Gramlich (1994a). A Constructor-Based Approach for Positive/Negative-Conditional Equational Specifications. J.  ... 
arXiv:0902.3614v1 fatcat:fl3fyfruqjewhlbjby3iyskmoy

The Explicit Definition of Quantifiers via Hilbert's epsilon is Confluent and Terminating [article]

Claus-Peter Wirth
2016 arXiv   pre-print
[ Wirth, 2015, Example 4.7 ] , [ Wirth, 2008, Example 8 ] .  ...  [ Wirth, 2009, Note 9 ] ). In CRS syntax (cf. e.g.  ... 
arXiv:1611.06389v1 fatcat:jhr5rn5rejbqla2k4dfymwrbaq

Shallow confluence of conditional term rewriting systems

Claus-Peter Wirth
2009 Journal of symbolic computation  
Clauses of this kind can be generated and proved automatically also for any other sort s instead of nat.  ...  Fritz (1945) and Wirth (2004 Wirth ( , 2005 .  ... 
doi:10.1016/j.jsc.2008.05.005 fatcat:zjp4ce43onbfxbt3sv5g5wndoq

Herbrand's Fundamental Theorem: The Historical Facts and their Streamlining [article]

Claus-Peter Wirth
2014 arXiv   pre-print
Heijenoort's [Heijenoort, 1975] at the beginning of § 2, besides the expansions used in this article (nowadays called "Herbrand expansions"), there is the alternative of Herbrand disjunctions used in [Wirth  ...  [Wirth &al., 2009, § 3.12, esp. Note 98] or [Wirth &al., 2014, § 14, esp.  ...  Today's calculi for proof search have an additional kind of free variables, called "free variables" in [ Fitting, 1996 ] , [ Wirth, 2013 ] , or "(free) γ-variables" in [ Wirth, 2004; .  ... 
arXiv:1405.6317v2 fatcat:5drkeurl3bhf3ki725ssbhoaji

A constructor-based approach for positive/negative-conditional equational specifications [chapter]

Claus-Peter Wirth, Bernhard Gramlich
1993 Lecture Notes in Computer Science  
The proofs, further concepts, and a deeper discussion can be found in Wirth&Gramlich 9].  ...  Moreover, an abstract inference system in the style of 1] for proving inductive (constructor) validity of rst-order clauses is given.  ...  Very recently, another method for inductive theorem proving of rst-order clauses has been developed in 4] along the lines of 2] by means of a transformational approach.  ... 
doi:10.1007/3-540-56393-8_15 fatcat:5ebvwgrgpngq3ksx5y4snpddbe

, , and Non-Permutability of -Steps

Claus-Peter Wirth
2012 Journal of symbolic computation  
And in Wirth (1998 Wirth ( , 2004 Wirth ( , 2008 Wirth ( , 2011 we have also added the notion of preservation of solutions.  ...  Wirth, , 2004 .  ... 
doi:10.1016/j.jsc.2011.12.035 fatcat:g2uh2ml62zgi7bnoffo74dczgi

Abstract notions and inference systems for proofs by mathematical induction [chapter]

Claus-Peter Wirth, Klaus Becker
1995 Lecture Notes in Computer Science  
The Analytic Approach The analytic approach was first formalized in Wirth (1991) .  ...  In Wirth (1991) this operational restriction is overcome by using a semantic foundedness notion.  ... 
doi:10.1007/3-540-60381-6_21 fatcat:wov5m7zlnrhrbpkovky2ezr6sm

Full First-Order Free Variable Sequents and Tableaux in Implicit Induction [chapter]

Claus-Peter Wirth
1999 Lecture Notes in Computer Science  
In Wirth (1997) we have presented a human-oriented inductive calculus for universally quanti ed clausal logic.  ...  Wirth & Becker (1995) , Wirth (1997) .  ...  Wirth (1997) , Wirth & Gramlich (1994) for more interesting classes for establishing inductive validities.  ... 
doi:10.1007/3-540-48754-9_25 fatcat:zrrwl5scz5e5xktk7a63cpt6z4

On notions of inductive validity for first-order equational clauses [chapter]

Claus-Peter Wirth, Bernhard Gramlich
1994 Lecture Notes in Computer Science  
We de ne and discuss various conceivable notions of inductive validity for rst-order equational clauses.  ...  As formulas to be proved we consider (implicitly universally quanti ed) rst-order clauses of the form A 1 ^: : : ^Am ?!  ...  This approach has a more general speci cation formalism permitting sets of rst-order clauses instead of constructor-based PNCTRSs.  ... 
doi:10.1007/3-540-58156-1_12 fatcat:b3cqt4wuajbzrffumllzch3a4q

David Poole's Specificity Revised [article]

Claus-Peter Wirth, Frieder Stolzenburg
2013 arXiv   pre-print
In the middle of the 1980s, David Poole introduced a semantical, model-theoretic notion of specificity to the artificial-intelligence community. Since then it has found further applications in non-monotonic reasoning, in particular in defeasible reasoning. Poole tried to approximate the intuitive human concept of specificity, which seems to be essential for reasoning in everyday life with its partial and inconsistent information. His notion, however, turns out to be intricate and problematic,
more » ... and problematic, which --- as we show --- can be overcome to some extent by a closer approximation of the intuitive human concept of specificity. Besides the intuitive advantages of our novel specificity ordering over Poole's specificity relation in the classical examples of the literature, we also report some hard mathematical facts: Contrary to what was claimed before, we show that Poole's relation is not transitive. The present means to decide our novel specificity relation, however, show only a slight improvement over the known ones for Poole's relation, and further work is needed in this aspect.
arXiv:1308.4943v4 fatcat:nkyh6fyppretplbm4mhap7hoji

A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications

Claus-Peter Wirth, Bernhard Gramlich
1994 Journal of symbolic computation  
Wirth (1991). intended congruence is then the intersection of all those maximally enlarged congruences.  ...  Dedication: To my father, Friedhelm Wirth, in gratefulness. A. The Proofs Proof of Lemma 5.4 We claim the following: (1) ?! R;X;!  ... 
doi:10.1006/jsco.1994.1004 fatcat:icf2mgkryzgqnoxunmndaqv6ee
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