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11
Equational abstractions
 of LNCS
, 2003
"... Abstract. Abstraction reduces the problem of whether an infinite state system satisfies version. The most common abstractions are quotients of the original system. We present a simple method of defining quotient abstractions by means of equations collapsing the set of states. Our method yields the m ..."
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Cited by 26 (12 self)
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Abstract. Abstraction reduces the problem of whether an infinite state system satisfies version. The most common abstractions are quotients of the original system. We present a simple method of defining quotient abstractions by means of equations collapsing the set of states. Our method yields the minimal quotient system together with a set of proof obligations that guarantee its executability and can be discharged with tools such as those in the Maude formal environment.
Certifying DomainSpecific Policies
, 2001
"... Proofchecking code for compliance to safety policies potentially enables a productoriented approach to certain aspects of software certification. To date, previous research has focused on generic, lowlevel programminglanguage properties such as memory type safety. In this paper we consider proof ..."
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Cited by 18 (3 self)
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Proofchecking code for compliance to safety policies potentially enables a productoriented approach to certain aspects of software certification. To date, previous research has focused on generic, lowlevel programminglanguage properties such as memory type safety. In this paper we consider proofchecking higherlevel domainspecific properties for compliance to safety policies. The paper first describes a framework related to abstract interpretation in which compliance to a class of certification policies can be efficiently calculated. Membership equational logic is shown to provide a rich logic for carrying out such calculations, including partiality, for certification. The architecture for a domainspecific certifier is described, followed by an implemented case study. The case study considers consistency of abstract variable attributes in code that performs geometric calculations in Aerospace systems.
Graphbased logic and sketches I: The general framework. Available by web browser from http://www.cwru.edu/1/class/mans/math/pub/wells
, 1996
"... Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic. ..."
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Cited by 8 (4 self)
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Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic.
Reasoning with Nondeterministic Specifications
 Polish Academy of Sciences, Institute of CS
, 1995
"... this paper we concentrate on a specification language that can be of use in both cases. We present a sound and complete Gentzenstyle deduction system for a logic that can be best (though rather informally) described as first order logic with inclusion and a let construct binding variables in nondet ..."
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Cited by 7 (2 self)
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this paper we concentrate on a specification language that can be of use in both cases. We present a sound and complete Gentzenstyle deduction system for a logic that can be best (though rather informally) described as first order logic with inclusion and a let construct binding variables in nondeterministic terms. We should also remark here that this paper presents a nontrivial firstorder extension of a calculus presented in [BK 95a]. It contains a detailed analysis of the phenomena related to empty carriers in multisorted environment. Also, we do not place any restrictions on the models, and allow for both empty carriers and partial functions. One may observe at this point that instead of multialgebras we might have used relational algebras. However, we prefer functions for the same reason that functions are present in first order logic  they are more intuitive in applications and have properties that make their use easier. Moreover, as it will be explained in the last section, we need "ordinary" algebras to be a special case of the formalism we develop.
An encoding of partial algebras as total algebras
 Information Processing Letters
"... We introduce a semantic encoding of partial algebras as total algebras through a Horn axiomatization of the existence equality relation interpreted as an algebraic operation. We show that this novel encoding enjoys several important properties that make it a good tool for the execution of partial al ..."
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Cited by 3 (2 self)
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We introduce a semantic encoding of partial algebras as total algebras through a Horn axiomatization of the existence equality relation interpreted as an algebraic operation. We show that this novel encoding enjoys several important properties that make it a good tool for the execution of partial algebraic specifications through means specific to ordinary algebraic reasoning, such as term rewriting.
Sketches: Outline with References
 Dept. of Computer Science, Katholieke Universiteit Leuven
, 1994
"... This document is an outline of the theory of sketches with pointers to the literature. An extensive bibliography is given. Some coverage is given to related areas such as algebraic theories, categorial model theory and categorial logic as well. An appendix beginning on page 11 provides definitions o ..."
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Cited by 2 (0 self)
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This document is an outline of the theory of sketches with pointers to the literature. An extensive bibliography is given. Some coverage is given to related areas such as algebraic theories, categorial model theory and categorial logic as well. An appendix beginning on page 11 provides definitions of some of the less standard terms used in the paper, but the reader is expected to be familiar with the basic ideas of category theory. A rough machine generated index begins on page 21. I would have liked to explain the main ideas of all the papers referred to herein, but I am not familiar enough with some of them to do that. It seemed more useful to be inclusive, even if many papers were mentioned without comment. One consequence of this is that the discussions in this document often go into more detail about the papers published in North America than about those published elsewhere. The DVI file for this article is available by anonymous FTP from ftp.cwru.edu in the directory
Reasoning with First Order Nondeterministic Specifications
"... The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multisorted algebras with setvalued operations, together with multisorted valuations of variables. We allow empty carrier sets but the valuations are kept total ..."
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Cited by 1 (0 self)
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The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multisorted algebras with setvalued operations, together with multisorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional let construct used for limiting nondeterminism. Atomic formulae are of the form t 1 ! t 2 where ! is a rewrite operator, corresponding semantically to inclusion. For the
A Categorical Approach to Logics and Logic Homomorphisms
, 2007
"... This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possib ..."
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This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possible to reason about maps from one logic to another in a consistent and convenient manner. By a consistent map is meant that the truth stays invariant, that is, a statement true in the source logic is mapped to a similarly true statement in the target logic. Conversely, a statement false in the source logic is mapped to a statement false in the target logic. While the thesis focuses on the theoretical notions outlined above, a brief coverage of two practical applications is given as a means to illustrate the utility of these notions. Concluding the text is a chapter containing a discussion and a section wherein possible future work is presented. In an effort to make the text mostly selfcontained, concepts beyond basic discrete mathematics are duly introduced with definitions and examples. These include, for
This document is available in various formats from the CoFI archives. 1 Copyright c○2002 CoFI, The Common Framework Initiative for Algebraic
, 2002
"... Permission is granted to anyone to make or distribute verbatim copies of this document, in any medium, provided that the copyright notice and permission notice are preserved, and that the distributor grants the recipient permission for further redistribution as permitted by this notice. Modified ver ..."
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Permission is granted to anyone to make or distribute verbatim copies of this document, in any medium, provided that the copyright notice and permission notice are preserved, and that the distributor grants the recipient permission for further redistribution as permitted by this notice. Modified versions may not be made. This is the formal semantics of version 1.0.2 of Casl. Although it is selfcontained, it is intended for readers who are already familiar with the main concepts of algebraic specification and with the Casl Language Summary. The structure of this document is deliberately identical to that of the Casl Language Summary to aid crossreference.