PROLOG.

A Description is Given of Prolog, a Contraction of Programming in Logic, Which Uses the Formalism of Mathematical Logic as its Primary Design Principle. the Structure of Prolog is Examined, and a Database Program is Described to Illustrate its application. an Application to an Artificial Intelligence Problem, the Towers of Hanoi, is Also Given

Finite Dimensional Group Rings

A Ring is Right Finite Dimensional If It Contains No Infinite Direct Sum of Right Ideals. We Prove that If a Group G is Finite, Free Abelian, or Finitely Generated Abelian, then a Ring R is Right Finite Dimensional If and Only If the Group Ring RG is Right Finite Dimensional. a Ring R is a Self-Injective Cogenerator Ring If Rn is Injective and RR is a Cogenerator in the Category of Unital Right /{-Modules; This Means that Each Right Unital A-Module Can Be Embedded in a Direct Product of Copies of R. Let G Be a Finite Group Where the Order of G is a Unit in R. Then the Group Ring RG is a Selfinjective Cogenerator Ring If and Only If R is a Self-Injective Cogenerator Ring. Additional Applications Are Given. © 1973 American Mathematical Society

A Parallel Array Scanning Algorithm

Suppose we are given a vector X of n real numbers and we want to find the maximum sum found in any contiguous subvector of X. In Jon Bentley\u27s article [l] on algorithm design and technique, a simple vector scanning problem and a series of progressively more efficient algorithms to solve this problem were discussed in some detail. Clearly, any algorithm must visit each location of X at least once and consequently a lower bound on the running time for problem is 0(n), which is in fact attainable as Bentley’s paper illustrates. However, the original motivation for this problem was the analagous two dimensional problem for an n x n array. That is, find the maximum sum contained in any contiguous rectangular subarray. Currently, the fastest algorithm obtained for this problem is O(n3)[2] ; the theoretical lower bound would be at least 0(n2). In this note, we will present a parallel processing approach to this problem which results in excess of one order of magnitude speed up for large problems in the 0(n3) algorithm

Finding Fixed Point Combinators using Prolog

A Powerful New Strategy, Called the Kernel Method, Has Been Developed by Larry Wos and William McCune at Argonne National Laboratories, to Study Various Fixed-Point Properties within Certain Classes of Applicative Systems. We Present a Very Simple Prolog Reasoning System, Named JIST, Which Incorporates Both Stages of the Kernel Method into a Single Unified Program. Furthermore, the Prolog Tool Has Been Extended to Run within a Distributed Environment using the Linda Protocol

Subsumption in Modal Logic

Subsumption has long been known as a technique to detect redundant clauses in the search space of automated deduction systems for classical first order logic. In recent years several automated deduction methods for non-classical modal logics have been developed. This thesis explores, how subsumption can be made to work in the context of these modal logic deduction methods. Many modern modal logic deduction methods follow an indirect approach. They translate the modal sentences into some other target language, and then determine whether there exists a proof in that language, rather than doing deduction in the modal language itself. Consequently, subsumption then needs to focus on the target language, in which the actual proof is done. World Path Logic (WPL) is introduced as a possible target language. Deduction in WPL works very much like in ordinary logic, the only significant difference is the need for a special purpose unification, which unifies world paths under an equational theory (E-unification). Relating WPL to a well understood first order logic of restricted quantification, the properties of WPL, that make deduction work, are examined. The obtained theoretical results are the basis for the following treatment of subsumption in WPL. Subsumption is analyzed treating a clause as a scheme standing for the set of its ground instances. Although the notion of ground instances in WPL is different from ordinary logic, it turns out that - just like in ordinary logic - a clause Cl subsumes another clause C2, if there exists a substitution 6 such that C10 £ C2. Once the special purpose unification has been implemented into a theorem prover to allow for deduction in WPL, existing subsumption tests then work without any further changes

Expectations for Associative-Commutative Unification Speedups in a Multicomputer Environment

An essential element of automated deduction systems is unification algorithms which identify general substitutions and when applied to two expressions, make them identical. However, functions which are associative and commutative, such as the usual addition and multiplication functions, often arise in term rewriting systems, program verification, the theory of abstract data types and logic programming. The introduction to the associative and commutative equality axioms together with standard unification brings with it problems of termination and unreasonably large search spaces. One way around these problems is to remove the troublesome axioms from the system and to employ a unification algorithm which unifies modulo the axioms of associativity and commutativity. Unlike standard unification, the associative-commutative (AC) unification of two expressions can lead to the formation of many most general unifiers. A report is presented on a hybrid AC unification algorithm which has been implemented to run in parallel on an Intel iPSC/

Development of an Expert System to Convert Knowledge-based Geological Engineering Systems into Fortran

A knowledge-based geographic information system (KBGIS) for geological engineering map (GEM) production was developed in GoldWorks, an expert system development shell. GoldWorks allows the geological engineer to develop a rule base for a GEM application. Implementation of the resultant rule base produced a valid GEM, but took too much time. This proved that knowledge-based GEM production was possible but in GoldWorks implementation failed as a practical production system. To solve this problem, a Conversion Expert System was developed which accepted, as input, a KBGIS and produced, as output, the equivalent Fortran code. This allowed the engineer to utilize GoldWorks for development of the rule base while implementing the rule base in a more practical manner (as a Fortran program). Testing of the Fortran program generated by this Conversion System confirmed that the GEMs produced were identical to those from the KBGIS, and execution time was significantly reduced. There was an additional benefit; since use of the Fortran program did not require access to the GoldWorks System, a single GoldWorks package could be used with the Conversion System to develop several Fortran production systems. These systems could then be used at remote production sites. However, each Fortran production system still required access to the Earth Resources Data Analysis System (ERDAS) that supplied the GIS input and output files. Thus, this Conversion System achieved two major objectives; it dramatically reduced GEM production time, and it added versatility