Knowledge Representation Applications Research Articles

Hypothetical revision and matter-of-fact supposition

The recent literature offers several models of the notion of matter of fact supposition1 revealed in the acceptance of the so-called indicative conditionals. Some of those models are qualitative [Collins 90], [Levi 96], [Stalnaker 84]. Other probabilistic models appeal either to infinitesimal probability or two place probability functions ([Adams 75], [van Fraassen 95], [Joyce 99], [McGee 94]). Recent work has made possible to understand which is the exact qualitative counterpart of the latter probabilistic models. In this article we show that the qualitative notion of change that thus arises is hypothetical revision, a notion previously axiomatized in [Arló-Costa 97] and [Arló-Costa & Thomason 96]. This notion is incompatible with AGM as well as with other standard methods of theory change (like Katsuno and Mendelzon's UPDATE). The way in which matter-of-fact supposition is modeled by hypothetical revision is illustrated via examples. The model is compared with other qualitative accounts of the notion of supposition encoded in two-place probability functions (like the one offered in [Hajek & Harper 96]), with models of subjunctive supposition, as well as with some of the well know models of learning. Applications in knowledge representation and in the theory of games and decisions are summarized.

Prioritized logic programming and its application to commonsense reasoning

Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce non-determinism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation.

The concept of evidence

We construct an explicatum of the evidence concept, evidence logic (EL), which is conceptually antecedent to classical logic (CL), having applications in knowledge representation and knowledge processing areas of artificial intelligence (AI), and satisfying Quinean concerns by not going beyond the simplicity (viz. Boolean algebraic structure) of CL, while implementing two requirements often present in AI domains: (1) that “absence of evidence” may well not be “evidence of absence” and (2) evidence gradations. For each integer n≥2, let size n−1 evidence space be linear order En={i/(n−1): i=1,…,n−1}. For each n≥2 and each logical similarity type τ, evidence logic ELn, τ is equipped with both confirmatory and refutatory predicate symbols Rc and Rr for each τ(i)-ary predicate, as well as evidence space En of evidence annotations for atomic formulas, while added to a usual set of logical axioms are axioms which assure that “stronger evidence strictly entails weaker evidence”; models of ELn, τ are similarly equipped, providing annotated confirmatory and refutatory relations interpreting each τ(i)-ary predicate. Trivializing all refutatory predicates in ELn, τ yields CELn, τ, confirmatory evidence logic; also EL2, τ is viewed as absolute evidence logic AELτ, while CEL2, τ is both confirmatory and absolute and is exactly classical logic CLτ. Let μ be monadic, stipulating p propositions, k constants, and u unary predicates; let μ′ be functional, obtained by adding to μ the stipulation of one unary function; and let ν be undecidable, stipulating a finite number of predicates and functions including at least one predicate or function which is at least binary or at least two unary functions. For theory T, let BSA(T) be the Boolean sentence algebra of T, let BA(σ) be the Boolean algebra with ordered basis of order type σ, and let ≅ denote “recursive isomorphism.” Consequences of previous work yield the characterization of EL: (1) BSA(ELn, μ)≅BA(ω⋅n2p⋅∑ski⋅n2ui) and BSA(CELn, μ)≅BA(ω⋅np⋅∑ski⋅nui), where ∑τi=1 if k=0, and ski are Stirling numbers of the second kind; (2) BSA(ELn, μ′)≅BA((ωω⋅η0+η0)⋅η0) and BSA(CELn, μ′)≅BA((ωω⋅η0+η0)⋅η0); (3) BSA(ELn, ν)≅BSA(CL〈2〉) and BSA(CELn, ν)≅BSA(CL〈2〉). ©2000 John Wiley & Sons, Inc.

HYPOTHETICAL REASONING ABOUT ACTIONS: FROM SITUATION CALCULUS TO EVENT CALCULUS

Hypothetical reasoning about actions is the activity of preevaluating the effect of performing actions in a changing domain; this reasoning underlies applications of knowledge representation, such as planning and explanation generation. Action effects are often specified in the language of situation calculus, introduced by McCarthy and Hayes in 1969. More recently, the event calculus has been defined to describe actual actions, i.e., those that have occurred in the past, and their effects on the domain. Altough the two formalisms share the basic ontology of atomic actions and fluents, situation calculus cannot represent actual actions while event calculus cannot represent hypotethical actions. In this article, the language and the axioms of event calculus are extended to allow representing and reasoning about hypothetical actions, performed either at the present time or in the past, altough counterfactuals are not supported. Both event calculus and its extension are defined as logic programs so that theories are readily adaptable for Prolog query interpretation. For a reasonably large class of theories and queries, Prolog interpretation is shown to be sound and complete w.r.t. the main semantics for logic programs.

In search of a “true” logic of knowledge: the nonmonotonic perspective

Modal logics are currently widely accepted as a suitable tool of knowledge representation, and the question what logics are better suited for representing knowledge is of particular importance. Usually, some axiom list is given, and arguments are presented justifying that suggested axioms agree with intuition. The question why the suggested axioms describe all the desired properties of knowledge remains answered only partially, by showing that the most obvious and popular additional axioms would violate the intuition. We suggest the general paradigm of maximal logics and demonstrate how it can work for nonmonotonic modal logics. Technically, we prove that each of the modal logics KD45, SW5, S4F and S4.2 is the strongest modal logic among the logics generating the same nonmonotonic logic. These logics have already found important applications in knowledge representation, and the obtained results contribute to the explanation of this fact.

Knowledge representation by conjunctive normal forms and disjunctive normal forms based on n-variable- m-dimensional fundamental clauses and phrases

In this paper, the n-variable-m-dimensional fundamental phrases and clauses are used to completely build the universal basis for the general CNF and DNF. Furthermore, the general n-variable-m-dimensional CNF and DNF are also defined in order to construct the generally standard expressions of different axiom-based CNFs and DNFs such as 11-axiom-based Boolean CNF and Boolean DNF, 9-axiom-based fuzzy CNF and fuzzy DNF, and 5-axiom-based t-norm- t-conorm CNF and t-norm- t-conorm DNF. Especially, the general algorithm to construct the general n-variable- m-dimensional CNF (DNF) from any given DNF (CNF) is proposed. In general, the intrinsic relations among the axioms, the space of the fundamental phrases (clauses), and the general CNF and DNF are briefly studied. Additionally, some interesting applications of knowledge representation by using the axiom-based CNF and DNF are also discussed. Finally, some new conclusions are drawn based on the new algorithm and the applications.

A Model for Medical Knowledge Representation Application to the Analysis of Descriptive Pathology Reports

A new knowledge-representation system is presented, designed for medical knowledge-based applications and in particular for the analysis of descriptive medical reports. Knowledge is represented at two levels. A definitional level uses a concept-type hierarchy, a relation-type hierarchy, and a set of schematic graphs to define the concepts used and the relations between them, as well as different types of cardinality restrictions on these relations. A set of compositional hierarchies using the classic "has-part" relation as well as a new set-inclusion relation allows concept composition to be precisely defined. An assertional level allows the creation and manipulation of empirical data, in the form of graphs using the concepts, relations, and constraints defined at the definition level. The use of cardinality constraints in graph unification is considered in the context of descriptive medical discourse analysis.

Representations of logic functions

Logic function representations play an important role in logic design and computer design, as well as VLSI design. There are many ways to represent a logic function. Presents and classifies 11 representation methods into “unique representation category” and “non‐unique representation category”. History of these methods is also briefly mentioned. There are three non‐unique representation methods: Boolean expression;sum of products; and product sums, and eight unique representation methods: truth table; canonical sum of products; canonical product of sums; sum of minterms; product of maxterms; Karnaugh map; Boolean lattice; and Venn diagram. A theorem is found which states that Boolean expression, sum of products, product of sums, sum of minterms, product of maxterms, and Karnaugh map, form a lattice structure. The results may have useful applications in knowledge representation, pictorial knowledge representation and other related areas.

Pictorial knowledge representation using pictorial semantic networks

SUMMARYClassifications of pictures and pictorial knowledge are presented. Pictorial knowledge is divided into three classes – angular pictorial knowledge, side pictorial knowledge, and angular and side pictorial knowledge. A block diagram of these three pictorial knowledge classes and a pictorial knowledge transformation module is also presented with illustrative examples. Pictorial semantic networks which in terms of pictorial nodes, property nodes, “is a” links, “has property” links, and “if and only if” links are introduced. Transitivity, generalization, specialization, inheritance hierarchy, and knowledge transformation properties are stated and illustrated by examples. Triangular, quadrangular, and polygonal knowledge representation using pictorial semantic networks are presented. The concepts of deducible property nodes are also presented with illustrative examples. Additional facts can be established from pictorial semantic networks. Thus, pictorial semantic networks are a useful way to represent pictorial knowledge in domains that use well-established taxonomies to simplify problem solving in pictorial information systems. Pictorial semantic networks offer what appears to be a fertile field for future study. The results may have useful applications in knowledge representation, expert systems, artificial intelligence, knowledge - based systems, pictorial information systems and related areas.