Razvan Diaconescu. The logic of Horn clauses is equational. Technical Report PRG-TR-3-93, Programming Research Group, University of Oxford, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....an indirect representation of partiality seems unreasonable. Although, having partial functions, semidecidable boolean relations can be easily simulated (at least if their falsity is never tested) by representing every relation as a boolean function, with a special boolean sort, see [8] and [9] for a similar approach in a total framework) predicates have been considered necessary, because of their recently increasing use in specifications, for example to represent transitions in concurrency, or the typing relation. In particular the use of predicates allows specifications of many ....

R. Diaconescu. The logic of Horn clauses is equational. Submitted for publication, 1992.

....is illustrated in [19] We note that the de nitions and results in this and the previous section extend to Horn clause logic with equality, by applying a construction that reduces that logic to hidden sorted equational logic. This is described in [19] extending some earlier work of Diaconescu [8]. 7 Concurrent Systems of Objects To motivate the general constructions that are given below, we rst consider a parallel connection of two simple objects: Example 29: We begin by de ning an integer cell X with the following OBJ3 code: 18 obj X is pr DATA . sort X . op init : X . op ....

Razvan Diaconescu. The logic of Horn clauses is equational. Technical Report PRG-TR-3-93, Programming Research Group, University of Oxford, 1993.

....an MSA signature obtained from the original first order signature by turning predicates into operations. Interpreting predicates as boolean valued operations is hardly new; it has even been used to lift narrowing to an operational semantics for logic programming [8] However, this approach (from [12]; see also [14, 13] is somewhat different, because it does not assume a full boolean structure on the new sort of truth values. Moreover, the model theoretic aspect is emphasised. A first order signature (S ; Sigma; Pi) consists of a many sorted signature (S ; Sigma) of function symbols, plus ....

Razvan Diaconescu. The logic of Horn clauses is equational. Technical Report PRG-TR-3-93, Programming Research Group, University of Oxford, 1990.

....a category Sys S . The category of domains is taken to be Set S , and the forgetful functor U S : Sys S Set S forgets the interpretations of the algebraic operations and the arrow composition, i.e. mapping each category to its set of arrows. Constraint Logic 13 Horn Clause Logic. In (Diaconescu, 1990) we introduce an embedding of the category of models M od S;P of a first order signature (S;S;P) as a retract of the category of algebras of an MSA signature (S b ; S b [P b ) obtained from the original first order signature by turning predicates into operations. Interpreting predicates as ....

Diaconescu, R. (1990). The logic of Horn clauses is equational. Technical Report PRG-TR-3-93, Programming Research Group, University of Oxford.

....form a category Sys6 . The category of domains is taken to be (the functor category) Cat S , and the forgetful functor U6 : Sys 6 Cat S forgets the interpretations of the algebraic operations only. Notice also that in this example the Simplifying Assumption does not hold. Horn Clause Logic. [8] introduces an embedding of the category of models of a first order signature (S ; 6;5) as a retract of the category of algebras of an MSA signature (S b ; 6 b [ 5 b ) obtained from the original first order signature by turning predicates into operations. Interpreting predicates as boolean ....

Razvan Diaconescu. The logic of Horn clauses is equational. Technical Report PRG-TR-3-93, Programming Research Group, University of Oxford, 1990.

....an MSA signature obtained from the original first order signature by turning predicates into operations. Interpreting predicates as boolean valued operations is hardly new; it has even been used to lift narrowing to an operational semantics for logic programming [5] However, this approach (from [7]; see also [9, 8] is somewhat different, because it does not assume a full boolean structure on the new sort of truth values. Moreover, the model theoretic aspect is emphasised. A first order signature (S; 6; 5) consists of a many sorted signature (S; 6) of function symbols, plus a family 5 = f5w ....

Razvan Diaconescu. The logic of Horn clauses is equational. Technical Report PRG-TR-3-93, Programming Research Group, University of Oxford, 1990.

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