A. Blikle. Three-valued predicates for software specification and validation. In R. Bloomfield, L. Marshall and R. Jones (eds.), VDM '88. VDM - The way ahead, Lecture Notes in Computer Science 328, pages 243--266, Berlin, 1988, Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... handles partial functions and undefined expressions [137] Two valued logics with undefined handles partial functions by introducing a constant (e.g. #) to represent an undefined value [122] Three valued logics with undefined allows the logical formulae to have the undefined value [11] [14] [68] 79] Some logics introduce even more than one special value, thus, leading to many valued logics [9] 10] Gries and Schneider modeled partial functions by under specified total functions to avoid undefinedness and their approach keeps the logic simple and calculational [56] JML adapts ....

A. Blikle. Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV:387--410, 1991.

....one bad apple spoils the barrel, an expression has the value as soon as it has a component with that value. This corresponds directly to the situation where instead of considering three valued total predicates one is considering two valued partial ones. However, as is frequently argued (cf. e.g. [Bl88]) this approach is not convenient in general in view of the following use of case constructors: Assume that we are given two total predicates P : D ft; fg and P 0 : D 0 ft; fg. Assuming furthermore that D and D 0 are disjoint, P and P 0 can be extended to functions from D[D 0 to T ....

A. Blikle. Three-valued predicates for software specification and validation. In R. Bloomfield, L. Marshall and R. Jones (eds.), VDM '88. VDM - The way ahead, Lecture Notes in Computer Science 328, 243--266, Springer-Verlag, Berlin, 1988.

....whereas in our calculus there is only one language level. We shall argue the advantage of our approach below. The logical combinators within the language (e.g. conjunction and universal quantification) are strict, and so are less than adequate for writing and reasoning about specifications (see [Bli88]) Norvell and Hehner [NH93] present a refinement calculus for expressions in which they seek to accommodate partiality and nondeterminacy. Their propositions are boolean expressions, but only deterministic ones are acceptable in the logic. The authors are aware of this shortcoming and list as ....

A. Blikle. Three-valued predicates for software specification and development. In R. et al. Bloomfield, editor, VDM --- the way ahead, volume 328 of Lecture Notes in Computer Science, pages 243--266. Springer Verlag, 1988.

.... we adopt the following truth tables for negation, conjunction, and disjunction: True False True False True False True True False True True True True False True False False False False False True False False True These connectives have a long pedigree, traced in [3]. They are monotonic in all arguments with respect to the partial ordering # that places below True and False. We also introduce strict equality which we denote by = operations are said to be strict if they yield whenever is an argument) Strict equality is also known as weak equality . ....

A. Blikle, Three-valued predicates for software specification and development, in: R. Bloomfield et al, ed., VDM --- the way ahead, Lecture Notes in Computer Science, vol 328 (Springer-Verlag, Berlin, 1988) 243-266.

....computations that go into infinite loops or cause errors. All other values are proper. In COLD K there is also a definedness predicate, D, that allows one to reason explicitly about whether a term denotes a proper value or not. There are several other languages with similar concepts [Bij90, Bli91, SKT95, KTB91, WDC 95] The second concept of protection we discuss is appropriate for BISLs that use a logic that does not admit the existence of partial functions, but uses underspecification. In such a logic, one avoids specifying a value for undefined terms [GS95, Jon95] In this ....

A. Blikle. Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV:387--410, 1991.

.... can be done naturally with many valued logic [67] Formal verification of such specifications leads to MVL deduction problems [28, 65] In software verification and mathematical applications, several approaches employ three valued logic to model partiality of programs and mathematical functions [20, 72, 74]. Natural Language Representation The idea to use deduction for solving the task of assigning meaning to natural language discourse is extensively studied in computational linguistics [70] Various ambiguity phenomena in natural language are best modelled with many valued logic [73] Databases ....

A. Blikle. Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV:387--410, 1991.

....as c is undefined otherwise. The other logical connectives and quantifiers are expressible by : and 9 in the classical way. The approach to the translation of logical expressions is connected with the treatment of three valued predicates in classical two valued logic which is described in [Bli88]. The translation is outlined by the following translation rules from the complete definition of the translation from VVSL to the extended COLD K, which is given in Chapter 3 of [BM88] h[ E ]i = some y 1 : B (forall y 2 : B ( h[E ]i = true , y 2 = false) and (h[E ]i = false , y 2 = true) y ....

A. Blikle. Three-valued predicates for software specification and validation. In R. Bloomfield, L. Marshall, and R. Jones, editors, VDM '88, pages 243--266. Springer Verlag, LNCS 328, 1988.

.... is demonstrated by the theorem provers which rely wholly or primarily upon it (eg Larch [13] and by the prominent place that rewriting tactics have in provers such as Isabelle [18] and HOL [9] The Logic of Partial Functions (LPF) handles undefined terms, and is the logic underlying VDM (see [4]) It has been mechanized in Isabelle by Agerholm Frost [1] Proofs in LPF could use standard rewriting of equal terms, but this would be complicated by the need to prove that the term to be rewritten is defined, since an undefined term is not equal to anything. In x2 we demonstrate that this ....

A. Blikle, Three-valued predicates for software specification and validation, in R. Bloomfield, L. Marshall & R. Jones, VDM --- The Way Ahead, Lecture Notes in Computer Science 328, 243--266.

....also models computations that go into infinite loops or cause errors. All other values are proper. In COLD K there is also a definedness predicate, D, that allows one to reason explicitly about whether a term denotes a proper value or not. There are several other languages with similar concepts [4, 6, 27, 21, 29]. The second concept of protection we discuss is appropriate for BISLs that use a logic that does not admit the existence of partial functions, but uses underspecification. In such a logic, one avoids specifying a value for undefined terms [14, 18] In this approach, to make a term undefined one ....

A. Blikle. Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV:387--410, 1991.

....one bad apple spoils the barrel, an expression has the value as soon as it has a component with that value. This corresponds directly to the situation where instead of considering three valued total predicates one is considering two valued partial ones. However, as is frequently argued (cf. e.g. [Bl88]) this approach is not convenient in general in view of the following use of case constructors: Assume that we are given two total predicates P : D ft; fg and P 0 : D 0 ft; fg. Assuming furthermore that D and D 0 are disjoint, P and P 0 can be extended to functions from D[D 0 to T ....

A. Blikle. Three-valued predicates for software specification and validation. In R. Bloomfield, L. Marshall and R. Jones (eds.), VDM '88. VDM - The way ahead, Lecture Notes in Computer Science 328, pages 243--266, Berlin, 1988, Springer-Verlag.

....of partial functions, and also models computations that go into infinite loops or cause errors. In COLD K there is also a definedness predicate, D, that allows one to reason explicitly about whether a term denotes a proper value or not. There are several other languages with similar concepts [4, 6, 26, 20, 28]. The second concept of protection we discuss is appropriate for BISLs that use a logic that does not admit the existence of partial functions, but uses underspecification. In such a logic, one avoids specifying a value for undefined terms [13, 17] In this approach, to make a term undefined one ....

A. Blikle. Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV:387--410, 1991.

.... undefined results of partial functions, and also models computations that go into infinite loops or cause errors. In COLD K there is also a definedness predicate, D, that allows one to explicitly reason about whether a term denotes a proper value or not. Other examples of this approach include [3, 4, 19, 26]. The second concept of protection we discuss is appropriate for BISLs that use a logic that does not admit the existence of partial functions, but uses underspecification. In such a logic, one avoids specifying a value for undefined terms [12, 16] In this approach, to make a term undefined one ....

A. Blikle. Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV:387--410, 1991.

No context found.

A. Blikle. Three-valued predicates for software specification and validation. In R. Bloomfield, L. Marshall and R. Jones (eds.), VDM '88. VDM - The way ahead, Lecture Notes in Computer Science 328, pages 243--266, Berlin, 1988, Springer-Verlag.

No context found.

A. Blikle. Three-valued predicates for software specification and validation. In [BMJ88], pages 243--266, 1988.

No context found.

Blikle, A. (1991) Three-valued predicates for software specification and validation. Fundamenta Informaticae, XIV, 387--410.

No context found.

A. Blikle. Three-valued predicates for software specification and validation. In [57], pages 243--266, 1988.

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