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Alloy: A Lightweight Object Modelling Notation
, 2001
"... Alloy is a little language for describing structural properties. It offers a declaration syntax compatible with graphical object models, and a setbased formula syntax powerful enough to express complex constraints and yet amenable to a fully automatic semantic analysis. Its meaning is given by tr ..."
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Cited by 339 (13 self)
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Alloy is a little language for describing structural properties. It offers a declaration syntax compatible with graphical object models, and a setbased formula syntax powerful enough to express complex constraints and yet amenable to a fully automatic semantic analysis. Its meaning is given by translation to an even smaller (formally defined) kernel. This paper presents the language in its entirety, and explains its motivation, contributions and deficiencies.
A Typed Logic of Partial Functions Reconstructed Classically
 ACTA INFORMATICA
, 1994
"... This paper gives a comprehensive description of a typed version of the logic known as LPF. This logic is basic to formal specification and verified design in the software development method VDM. If appropriately extended to deal with recursively defined functions, the data types used in VDM, etc ..."
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Cited by 31 (3 self)
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This paper gives a comprehensive description of a typed version of the logic known as LPF. This logic is basic to formal specification and verified design in the software development method VDM. If appropriately extended to deal with recursively defined functions, the data types used in VDM, etc., it gives the VDM notation and its associated rules of reasoning. The paper provides an overview of the needed extensions and examines some of them in detail. It is shown how this nonclassical logic  and the extensions  can be reconstructed classically by embeddings into classical infinitary logic.
Avoiding the Undefined by Underspecification
 Computer Science Today: Recent Trends and Developments, number 1000 in Lecture Notes in Computer Science
, 1995
"... We use the appeal of simplicity and an aversion to complexity in selecting a method for handling partial functions in logic. We conclude that avoiding the undefined by using underspecification is the preferred choice. ..."
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Cited by 25 (0 self)
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We use the appeal of simplicity and an aversion to complexity in selecting a method for handling partial functions in logic. We conclude that avoiding the undefined by using underspecification is the preferred choice.
Semantics of Inheritance and Attributions in the Description System Omega
, 1982
"... Omega is a description system for knowledge embedding which incorporates some of the attractive modes of expression in common sense reasoning such as descriptions, inheritance, quantification, negation, attributions and multiple viewpoints. A forrealization of Omega is developed as a framework fi)r ..."
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Cited by 8 (0 self)
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Omega is a description system for knowledge embedding which incorporates some of the attractive modes of expression in common sense reasoning such as descriptions, inheritance, quantification, negation, attributions and multiple viewpoints. A forrealization of Omega is developed as a framework fi)r investigations on the foundations of knowledge .representation. As a logic, Omega achieves the goal of an intuitively sound and consistent theory of classes which permits unrestricted abstraction within a powertiff logic system. Description abm'actio is the construct provided in Omega corresponding to sct abstraction. Altributions and inheritance are the basic mechanisms for knowledge structuring. To achieve flexibility and incrcmentality, the language allows descriptions with an arbitrary number of attributions, rather dacn predicates with a fixed number of arguments as in predicate logic. This requires a peculiar interpretation for istace descriptions, which in turn provides insights into the use and meaning of several kind of attributions. The Formal treatcmcnt consists in presenting semantic models for Omega, derMng an axiomatization and estblishing the consistency and completeness of the logic.
Definitions in Nonstrict Positive Free Logic
 Modern Logic
, 1997
"... Every "practical" programming language supplies the programmer with at least one nonstrict construct, such as the ALGOL60 arithmetic `ifthen else' and the LISP `cond'. Many programming languages also enable the user to define nonstrict functions. In some languages, this is accomplished through the ..."
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Cited by 4 (2 self)
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Every "practical" programming language supplies the programmer with at least one nonstrict construct, such as the ALGOL60 arithmetic `ifthen else' and the LISP `cond'. Many programming languages also enable the user to define nonstrict functions. In some languages, this is accomplished through the lazy evaluation of procedure parameters, as realized, for example, by the callbyname devices of ALGOL60 and SIMULA67 and the callbyneed mechanism of Haskell. In other languages, such as Common LISP, a macro definition facility can serve a similar purpose. Programming languages that provide a mechanism for the user to define nonstrict functions are nonstrict languages, and we call the natural underlying logic of these languages nonstrict positive free logic. In this paper, we present the definition theory of nonstrict positive free logic. Suitable transformations of sentences in standard logic into sentences in nonstrict positive free logic preserve many properties of definitions in stand...
Model Sets in a Nonconstructive Logic of Partial Terms with Definite Descriptions
 Springer LNAI
, 2000
"... The logic of partial terms (LPT) is a variety of negative free logic. In LPT, functions, as well as predicates, are strict, and free variables are given the generality interpretation. Both nonconstructive (classical) and intuitionist brands of negative free logic have served in foundational investig ..."
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Cited by 3 (0 self)
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The logic of partial terms (LPT) is a variety of negative free logic. In LPT, functions, as well as predicates, are strict, and free variables are given the generality interpretation. Both nonconstructive (classical) and intuitionist brands of negative free logic have served in foundational investigations, and Hilbertstyle axiomatizations, natural deduction systems, and Gentzenstyle sequents have been developed for them. This paper focuses on nonconstructive LPT with denite descriptions, called LPD, lays the foundation for tableaux systems by dening the concept of an LPD model system and establishing Hintikka's Lemma, and summarizes the corresponding tableaux proof rules. Philosophical Roots of Negative Free Logics ... not even with these (contraries `Socrates is well' and `Socrates is sick') is it necessary always for one to be true and the other false. For if Socrates exists one will be true and the other false, but if he does not both will be false.... (Aristotle, Categories, x, 13b12) A robust sense of reality is necessary in framing a correct analysis of propositions about ... round squares and other such pseudoobjects....we shall insist that in the analysis of propositions, nothing \unreal" is to be admitted. (Bertrand Russell,
A Free Logical Foundation for Nonstrict Functions
"... this paper, we sketch the definition theory for a nonstrict positive free logic in which there is exactly one error object err to which all terms without existential import can refer. Having exactly one error object identifies nontermination and all runtime errors. This is most natural in languages ..."
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this paper, we sketch the definition theory for a nonstrict positive free logic in which there is exactly one error object err to which all terms without existential import can refer. Having exactly one error object identifies nontermination and all runtime errors. This is most natural in languages such as Miranda and haskell in which execution is aborted immediately when an error is raised [16]. By using a free logic, we are able to state the axioms of a mathematical theory without cluttering the axiomatization with error conditions, as would be required using restricted quantification in standard logic. For example, Peano's axiom:
What is Frege’s Theory of Descriptions?
"... When prompted to consider Frege’s views about definite descriptions, many philosophers think about the meaning of proper names, and some of them can cite the following quotation taken from a footnote Frege’s 1892 article “ Über Sinn und Bedeutung.”2 ..."
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Cited by 1 (1 self)
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When prompted to consider Frege’s views about definite descriptions, many philosophers think about the meaning of proper names, and some of them can cite the following quotation taken from a footnote Frege’s 1892 article “ Über Sinn und Bedeutung.”2
Functional Monadic Bounded Algebras
, 2010
"... The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomor ..."
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The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by the disjunction of the equations ∃E = 1 and ∃E = 0. We also define a weaker notion of “relatively functional ” algebra, and show that every member of MBA is isomorphic to a relatively functional one. In [1], an equationally defined class MBA of monadic bounded algebras was introduced. Each of these algebras comprises a Boolean algebra B with a distinguished element E, thought of as an existence predicate, and an operator ∃ on B reflecting the properties of the existential quantifier in logic without existence assumptions. MBA was shown to be generated by a certain proper
A Sound and Complete SOSSemantics for NonDistributed Deterministic Abstract State Machines
"... In this paper we present a sound and complete Structural Operational Semantics (SOS) for nondistributed deterministic Abstract State Machines (ASMs). Since ASMs exhibit both sequential and parallel features, the semantics is structured into two layers. One layer describes the parallel execution of ..."
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In this paper we present a sound and complete Structural Operational Semantics (SOS) for nondistributed deterministic Abstract State Machines (ASMs). Since ASMs exhibit both sequential and parallel features, the semantics is structured into two layers. One layer describes the parallel execution of updates, the other layer describes the sequential execution of rules. The semantics has some nice properties, the most important of which include soundness and completeness.