Logic programming with polymorphically order-sorted types

Smolka, Gert

doi:10.1007/3-540-50667-5_58

Cited by 57 publications

(59 citation statements)

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“…Alternatively, order-sorted logic has been recognized as a tool for providing a logical knowledge representation language for taxonomic knowledge [1]- [3], [7], [11], [13]- [15]. This logical language contains a sort-hierarchy that is used to represent domain-specific ontologies; however, there is a gap between formal ontology and logical languages because the meta-properties axiomatized in formal ontology are not easily embedded in the specifications of logical languages, such as syntax and semantics.…”

Section: Time and Situation Dependenciesmentioning

confidence: 99%

A Time and Situation Dependent Semantics for Ontological Property Classification

Kaneiwa

Mizoguchi

2011

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper proposes a new semantics that characterizes the time and/or situation dependencies of properties, together with the ontological notion of existential rigidity. For this purpose, we present ordersorted tempo-situational logic (OSTSL) with rigid/anti-rigid sorts and an existential predicate. In this logic, rigid/anti-rigid sorted terms enable the expressions for sortal properties, and temporal and situational operators suitably represent the ontological axioms of existential rigidity and time and/or situation dependencies. A specific semantics of OSTSL adheres to the temporal and situational behaviors of properties based on existential rigidity. As a result, the semantics guarantees that the ontological axioms of properties expressed by sorted tempo-situational formulas are logically valid.

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Section: Time and Situation Dependenciesmentioning

confidence: 99%

A Time and Situation Dependent Semantics for Ontological Property Classification

Kaneiwa

Mizoguchi

2011

IEICE Trans. Inf. & Syst.

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“…Smolka uses type rewriting [28], partial order on type symbols is used by [3,12], Hanus proposes more general equational type specifications [10] and also Horn clauses for the subtype relation [9]. Naish uses Prolog clauses to define polymorphic predicates [22]; the predicate type is specified by some general constraint expression in [13], and so on.…”

Section: Problems Of Polymorphic Type Systems With Subtypesmentioning

confidence: 99%

“…is usually not detected as ill-typed (see e.g. [28,12]) although it is logically equivalent to q1! If the type parameter T in the declaration '=': T x T is substituted by person, then X = Xm is not ill-typed, because the variable X has type male which is a subtype of person, and the same applies to the type female of the variable Xm.…”

Section: Examplementioning

confidence: 99%

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Using Types as Approximations for Type Checking Prolog Programs

Beierle

Meyer²

1999

Functional and Logic Programming

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Abstract. Subtyping tends to undermine the effects of parametric polymorphism as far as the static detection of type errors is concerned. Starting with this observation we present a new approach for type checking logic programs to overcome these difficulties. The two basic ideas are, first, to interpret a predicate type declaration as an approximation for the success set of the predicate. Second, declarations are extended with type constraints such that they can be more refined than in other conventional type systems. The type system has been implemented in a system called Typical which provides a type checker for Standard Prolog enriched with type annotations.

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“…The Java 5.0 type unification problem is given as: For two type terms θ 1 , θ 2 a substitution is demanded, such that σ( θ 1 ) ≤ * σ( θ 2 ), where ≤ * is the Java 5.0 subtyping relation. The type system of Java 5.0 is very similar to the type system of polymorphically order-sorted types, which is considered for the logical language TEL [5] and for the functional object-oriented language OBJ-P [6]. In [5] the type unification problem is mentioned as an open problem.…”

Section: Introductionmentioning

confidence: 99%

Java Type Unification with Wildcards

Plümicke¹

2009

Lecture Notes in Computer Science

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Abstract. With the introduction of Java 5.0 the type system has been extended by parameterized types, type variables, type terms, and wildcards. As a result very complex types can arise. The term Vector>> is for example a correct type in Java 5.0. In this paper we present a type unification algorithm for Java 5.0 type terms. The algorithm unifies type terms, which are in subtype relationship. For this we define Java 5.0 type terms and its subtyping relation, formally. As Java 5.0 allows wildcards as instances of generic types, the subtyping ordering contains infinite chains. We show that the type unification is still finitary. We give a type unification algorithm, which calculates the finite set of general unifiers.

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Logic programming with polymorphically order-sorted types

Cited by 57 publications

References 10 publications

A Time and Situation Dependent Semantics for Ontological Property Classification

A Time and Situation Dependent Semantics for Ontological Property Classification

Using Types as Approximations for Type Checking Prolog Programs

Java Type Unification with Wildcards

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