Computing cost estimates for proof strategies

In this paper we extend work of Treitel and Genesereth for calculating cost estimates for alternative proof methods of logic programs. We consider four methods: (1) forward chaining by semi-naive bottom-up evaluation, (2) goal-directed forward chaining by semi-naive bottom-up evaluation after Generalized Magic-Sets rewriting, (3) backward chaining by OLD resolution, and (4) memoing backward chaining by OLDT resolution. The methods can interact during a proof. After motivating the advantages of each of the proof methods, we show how the effort for the proof can be estimated. The calculation is based on indirect domain knowledge like the number of initial facts and the number of possible values for variables. From this information we can estimate the probability that facts are derived multiple times. An important valuation factor for a proof strategy is whether these duplicates are eliminated. For systematic analysis we distinguish between in costs and out costs of a rule. The out costs correspond to the number of calls of a rule. In costs are the costs for proving the premises of a clause. Then we show how the selection of a proof method for one rule influences the effort of other rules. Finally we discuss problems of estimating costs for recursive rules and propose a solution for a restricted case

Combining terminological and rule-based reasoning for abstraction processes

Terminological reasoning systems directly support the abstraction mechanisms generalization and classification. But they do not bother about aggregation and have some problems with reasoning demands such as concrete domains, sequences of finite but unbounded size and derived attributes. The paper demonstrates the relevance of these issues in an analysis of a mechanical engineering application and suggests an integration of a forward-chaining rule system with a terminological logic as a solution to these problems

Bidirectional reasoning of horn clause programs : transformation and compilation

A compilative approach for forward reasoning of horn rules in Prolog is presented. Pure horn rules - given as Prolog clauses - are to be used for forward and backward reasoning. These rules are translated into Prolog clauses, denoting one forward reasoning step. Forward chaining is triggered by an initial fact, from which the consequences are derived. Premises of forward rules are verified by Prolog's backward proof procedure using the original clauses. Thus, without any changes to the Prolog interpreter integrated bidirectional reasoning of the original horn rules is possible. Breadth-first and depth-first reasoning strategies with enumeration and collection of conclusions are implemented. In order to translate forward clauses into WAM operations several improvements are introduced. To avoid inefficient changes of program code derived facts are recorded in a special storage area called retain stack. Subsumption of a new conclusion by previously derived facts is tested by a built-in procedure. As a reasonable application of this kind of forward reasoning its use is demonstrated for integrity constraint checking

Integrating bottom-up and top-down reasoning in COLAB

The knowledge compilation laboratory COLAB integrates declarative knowledge representation formalisms, providing source-to-source and source-to-code compilers of various knowledge types. Its architecture separates taxonomical and assertional knowledge. The assertional component consists of a constraint system and a rule system, which supports bottom-up and top-down reasoning of Horn clauses. Two approaches for forward reasoning have been implemented. The first set-oriented approach uses a fixpoint computation. It allows top-down verification of selected premises. Goal-directed bottom-up reasoning is achieved by a magic-set transformation of the rules with respect to a goal. The second tuple-oriented approach reasons forward to derive the consequences of an explicitly given set of facts. This is achieved by a transformation of the rules to top-down executable Horn clauses. The paper gives an overview of the various forward reasoning approaches, their compilation into an abstract machine and their integration into the COLAB shell

SASLOG : Lazy Evaluation Meets Backtracking

We describe a combined functional / logic programming language SASLOG which contains Turner’s SASL, a fully lazy, higher-order functional language, and pure Prolog as subsets. Our integration is symmetric, i.e. functional terms can appear in the logic part of the program and v.v. Exploiting the natural correspondence between backtracking and lazy streams yields an elegant solution to the problem of transferring alternative variable bindings to the calling functional part of the program. We replace the rewriting approach to function evaluation by combinator graph reduction, thereby regaining computational efficiency and the structure sharing properties. Our solution is equally well suited to a fixed combinator set and to a super combinator implementation. In the paper we use Turner's fixed combinator set

COLAB : a hybrid knowledge representation and compilation laboratory

Knowledge bases for real-world domains such as mechanical engineering require expressive and efficient representation and processing tools. We pursue a declarative-compilative approach to knowledge engineering. While Horn logic (as implemented in PROLOG) is well-suited for representing relational clauses, other kinds of declarative knowledge call for hybrid extensions: functional dependencies and higher-order knowledge should be modeled directly. Forward (bottom-up) reasoning should be integrated with backward (top-down) reasoning. Constraint propagation should be used wherever possible instead of search-intensive resolution. Taxonomic knowledge should be classified into an intuitive subsumption hierarchy. Our LISP-based tools provide direct translators of these declarative representations into abstract machines such as an extended Warren Abstract Machine (WAM) and specialized inference engines that are interfaced to each other. More importantly, we provide source-to-source transformers between various knowledge types, both for user convenience and machine efficiency. These formalisms with their translators and transformers have been developed as part of COLAB, a compilation laboratory for studying what we call, respectively, "vertical\u27; and "horizontal\u27; compilation of knowledge, as well as for exploring the synergetic collaboration of the knowledge representation formalisms. A case study in the realm of mechanical engineering has been an important driving force behind the development of COLAB. It will be used as the source of examples throughout the paper when discussing the enhanced formalisms, the hybrid representation architecture, and the compilers

Combining terminological and rule-based reasoning for abstraction processes

Terminological reasoning systems directly support the abstraction mechanisms generalization and classification. But they do not bother about aggregation and have some problems with reasoning demands such as concrete domains, sequences of finite but unbounded size and derived attributes. The paper demonstrates the relevance of these issues in an analysis of a mechanical engineering application and suggests an integration of a forward-chaining rule system with a terminological logic as a solution to these problems

AAAI-MAKE 2022 : machine learning and knowledge engineering for hybrid intelligence

The AAAI 2022 Spring Symposium on Machine Learning and Knowledge Engineering for Hybrid Intelligence (AAAI-MAKE 2022) brought together researchers and practitioners of the two fields to reflect on advances in combining them, and to present the first results in creating hybrid intelligence with the two AI methods. AAAI-MAKE 2022 is the fourth consecutive edition of this symposium, which combines two prominent AI approaches, symbolic and sub-symbolic AI, as hybrid AI.http://ceur-ws.orgam2023Informatic