Decidable reasoning between ontologies and rules is required for the Semantic Web. This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe order-sorted logic programming with sort, predicate, and metapredicate hierarchies for deriving predicate and meta-predicate assertions. Meta-level predicates (predicates of predicates) are u...

The problem of merging two intransitive sorted sequences that is to generate a sorted total order without the transitive property is considered A cost optimal parallel merging algorithm is proposed under the EREW PRAM model This algorithm has a run time of O log n using O n log n processors The cost optimal merge in the strong sense is still an open problem

Questions about order versus disorder in systems and models have been fascinating scientists over the years. In Computer Science, order is intimately related to sorting, commonly meant as the task of arranging keys in increasing or decreasing order with respect to an underlying total order relation. The sorted organization is amenable for searching a set of n keys, since each search requires Θ(...

Abstract Neo-Fregean logicists claim that Hume’s Principle ( HP ) may be taken as an implicit definition of cardinal number, true simply by fiat. A long-standing problem for neo-Fregean logicism is not deductively conservative over pure axiomatic second-order logic. This seems to preclude from being In this paper, we study Richard Kimberly Heck’s Two-Sorted Frege Arithmetic 2FA ), a variation o...

We present TRIM, an abstract machine capable of executing a subset of the algebraic speci cation language OBJ3. A speci cally designed compiler translates the order sorted conditional equations of an OBJ3 speci cation into TRIM code. The fact that TRIM supports order sorted term rewriting natively di erentiates it from many other abstract term rewriting machines. To obtain more e cient abstract...

This paper proposes a simple, set-theoretic framework providing expressive typing, higher-order functions and initial models at the same time. Building upon Russell’s ramified theory of types, we develop the theory of R-logics, which are axiomatisable by an order-sorted equational Horn logic with a membership predicate, and of G-logics, that provide in addition partial functions. The latter are...

ICT has been exploring the application of the limited-order blocksort [1MS] to lossy and lossless image compression. The method used to predict values is similar to Binary Tree Predictive Coding (BTPC) [2JR]. In BTPC, the quantized prediction errors are encoded using static Huffman coding. The ICT coder establishes a sorting order based on each pixel's context and applies the limited-order bloc...

The usage of sorts in first-order automated deduction has brought greater conciseness of representation and a considerable gain in efficiency by reducing the search spaces involved. This suggests that sort information can be employed in higher-order theorem proving with similar results. This thesis develops a sorted higher-order logic ΣHOL suitable for automatic theorem proving applications. ΣH...

This paper studies several applications of the notion of a presentation of a functor by operations and equations. We show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a ca...