Showing papers on "Class (philosophy) published in 1991"

The well-founded semantics for general logic programs

Abstract: A general logic program (abbreviated to "program" hereafter) is a set of roles that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) slttmg above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program, " or Its "declarative semantics. " Ideally, queries directed to the program would be answered in accordance with this model. Recent research indicates that some programs do not have a "satisfactory" total model; for such programs, the question of an appropriate partial model arises. Unfounded sets and well-founded partial models are introduced and the well-founded semantics of a program are defined to be its well-founded partial model. If the well-founded partial model is m fact a total model. it is called the well-founded model. It n shown that the class of programs possessing a total well-founded model properly includes previously studied classes of "stratified" and "locally stratified" programs, The method in this paper is also compared with other proposals in the literature, including Clark's "program completion, " Fitting's and Kunen's 3-vahred interpretations of it, and the "stable models" of Gelfond and Lifschitz.

The General, the Abstract, and the Generic in Advanced Mathematics

Abstract: ion An abstraction process occurs when the subject focuses attention on specific properties of a given object and then considers these properties in isolation from the original This might be done, for example, to understand the essence of a certain phenomenon, perhaps later to be able to apply the same theory in other cases to which it applies Such application of an abstract theory would be a case of reconstructive generalization – because the abstracted properties are reconstructions of the original properties, now applied to a broader General, Abstract and Generic Guershon Harel & David Tall – 4 – domain However, note that once the reconstructive generalization has occurred, it may then be possible to extend the range of examples to which the arguments apply through the simpler process of expansive generalization For instance, when the group properties are extracted from various contexts to give the axioms for a group, this must be followed by the reconstruction of other properties (such as uniqueness of identity and of inverses) from the axioms This leads to the construction of an abstract group concept which is a re-constructive generalization of various familiar examples of groups When this abstract construction has been made, further applications of group theory to other contexts (usually performed by specialization from the abstract concept) are now expansive generalizations of the original ideas The case of definition The process of formal definition in advanced mathematics actually consists of two distinct complementary processes One is the abstraction of specific properties of one or more mathematical objects to form the basis of the definition of the new abstract mathematical object The other is the process of construction of the abstract concept through logical deduction from the definition The first of these processes we will call formal abstraction, in that it abstracts the form of the new concept through the selection of generative properties of one or more specific situations; for example, abstracting the vector-space axioms from the space of directed-line segments alone or from what it is noticed to be common to this space and the space of polynomials This formal abstraction historically took many generations, but is now a preferred method of progress in building mathematical theories The student rarely sees this part of the process Instead (s)he is presented with the definition in terms of carefully selected properties as a fait accomplit When presented with the definition, the student is faced with the naming of the concept and the statement of a small number of properties or axioms But the definition is more than a naming It is the selection of generative properties suitable for deductive construction of the abstract concept The abstract concept which satisfies only those properties that may be deduced from the definition and no others requires a massive reconstruction Its construction is guided by the properties which hold in the original mathematical concepts from which it was abstracted, but judgement of the truth of these properties must be suspended until they are deduced from the definition For the novice this is liable to cause great confusion at the time The newly constructed abstract object will then generalize the General, Abstract and Generic Guershon Harel & David Tall – 5 – properties embodied in the definition, because any properties that may be deduced from them will be part of it Because of the difficulties involved in the construction process, this is a reconstructive generalization Occasionally the process leads to a newly constructed abstract object whose properties apply only to the original domain, and not to a more general domain For instance, the formal abstraction of the notion of a complete ordered field from the real numbers, or the abstraction of the group concept from groups of transformations Up to isomorphism there is only one complete ordered field, and Cayley’s theorem shows that every abstract group is isomorphic to a group of transformations In these cases the process leads to an abstract concept which does not extend the class of possible embodiments We include these instances within the same theoretical framework for, though they fail to generalize the notion to a broader class of examples, they very much change the nature of the concept in question The formal abstraction process coupled with the construction of the formal concept, when achieved, leads to a mental object that is easier for the expert to manipulate mentally because the precise properties of the concept have been abstracted and can lead to precise general proofs based on these properties Formal abstraction leading to mathematical definitions usually serves two purposes which are particularly attractive to the expert mathematician: (a) Any arguments valid for the abstracted properties apply to all other instances where the abstracted properties hold, so (provided that there are other instances) the arguments are more general (b) Once the abstraction is made, by concentrating on the abstracted properties and ignoring all others, the abstraction should involve less cognitive strain These two factors make a formal abstraction a powerful tool for the expert yet – because of the cognitive reconstruction involved – they may cause great difficulty for the learner

Coastal Marine Zooplankton:A Practical Manual for Students

Abstract: Preface Phylum "sarcomastigophora" (protozoa) Class "dinoflagellida" Phylum "cnidaria" Class "hydrozoa" Class "scyphozoa" Phylum "ctenophora" Class "tentaculata" Class "nuda" Phylum "nemertea" Phylum "annilida" Class "polychaeta" Phylum "arthropoda" Class "crustacea" Phylum "chaetognatha" Phylum "bryozoa" Class "gymnolaemata" Phylum "phoronida" Phylum "mollusca" Class "polyplacophora" Class "gastropoda" Class "lamellibranchia" Class "cephalopoda" Phylum "echinodermata" Class "asteroidea" Class "ophiuroidea" Class "echinoidea" Phylum "hemichordata" Class "enteropneusta" Phylum "urochordata" Class "larvacea" Class "ascidiacea" Class "thaliacea" Phylum "chordata" Class "osteichthyes"

Entity/relationship to object oriented logical model conversion method

Abstract: A method for automatically translating computer application program modeling data expressed in entity/relationship terminology into computer application program model data expressed in object oriented terminology. A conversion process extracts unique entity names from the E/R model database and converts the entity names so found into object oriented class names. Next, based on the type of entity/relationships found in the E/R data model, target and source entities are identified for each "is a" type of relationship and the converted object oriented class names are arranged in a hierarchical inheritance grouping in which each unique class name whose matching entity name is the source of a "is a" relationship is subordinate to the unique object class name in the hierarchy which matches the target entity name is said "is a" relationship and in which grouping any unique object class name that has no matching entity with an "is a" relationship is placed subordinate to an arbitrarily selected unique object class name.

Pro-attitudes and direction of fit

Abstract: What amounts to a general account of the class of mental states which have come to be labeled "pro-attitudes" has recently been suggested by Michael Smith (1987). His idea is that we can best understand these as being states "with which the world must fit" and that we can explicate this "direction of fit" metaphor in terms of certain sorts of dispositions of the person who has the state in question. In this paper I want to examine Smith's suggestion. This account of pro-attitudes comes in the context of a defense of the Humean theory of motivation which, according to Smith, can be expressed as follows: "R at t constitutes a motivating reason of agent A to 4 iff there is some v such that R at t consists of a desire of A to P and a belief that were he to 1 he would "' (p. 36). If this theory is to be true it must include a method for ruling out the sort of case where it is claimed that it was a person's mere belief that moved him to do it. Smith tries to do this by arguing for two distinct points. First, he argues that explanations of actions in terms of the agent's reasons are essentially teleological explanations, that is, they are explanations which represent the action as an attempt by the agent to achieve some purpose or goal. So the issue is simply whether the Humean theory is better able to make sense of motivation as pursuit of a goal (p. 44). That this is so, he claims, and this is his second point, will be clear once we understand that only desires, broadly understood, are the right sorts of "mental objects" to make sense of such teleological explanations. The basic idea is that mental states can have one of two possible "directions of fit".' Beliefs are the exemplars of mental states with "mind-to-world" direction of fit since they aim at being true, i.e., "matching the world". If there is a mismatch between a belief and reality then it is the belief which has failed; it has failed to "fit" the world. Desires, on the other side, are exemplars of "world-to-mind" direction of fit. They aim at satisfaction or realization, not truth. If a desire fails to "fit" the world, that is not any defect in the desire. It merely shows that the world needs to be changed if the desire is to be realized. Smith seems correct in holding that "[h]aving a motivating reason is, inter alia, having a goal" (p. 55). The idea of direction of fit of mental states then lets us see, Smith thinks, that having a goal is nothing more than being in a mental state with a world-to-mind direction of fit. "[W]hat kind of state is the having of

Classes are states of affairs

Abstract: In his monograph Parts of Classes (1991), David Lewis argues that mereology, the calculus of whole and part, applies to classes. What are the parts of classes on his view? They are all classes themselves: subclasses of the classes in question. It follows that singletons, that is, unit classes (I will use the two phrases interchangeably), are mereological atoms. This enables Lewis to define class membership in a striking new way. The relation of member to its singleton is taken as primitive. Membership of classes generally is then defined by saying that x is a member of a class y if and only if the singleton of x is a part of y. ' This leads him to focus his attention onto the relation of member to singleton. He finds it a very mysterious one. At the present stage of philosophical enquiry it is a pretty mysterious relation on anybody's view. But it is particularly mysterious for Lewis. He argues thus. If a singleton class is a mereological atom, then it can have no internal structure. Very many members of singletons will have an internal structure, some a very complex internal structure. But in each case the singleton itself will have no internal structure. Using this lack of structure as a premiss, Lewis draws the conclusion that singletons are "wholly distinct" from their members. This conclusion of Lewis's appears to involve taking up one of at least three positions about the location of classes: (i) they are not located, except perhaps at structureless points or point-instants; (ii) they are located where their members are located, but are not located where the proper parts of these members are located; (iii) they are located-wholly-where each part, proper or improper, of their members is located. I am not sure that solutions (ii) and (iii) are available where the member is a relation, at any rate where relations are not reduced in some way (say to classes!). All these views seem rather unattractive. But a more important problem for Lewis is this. Member and singleton are wholly distinct. Yet it appears to be a necessary truth that, given an individual, its singleton exists. And is it not still more obviously a necessary truth that, given a singleton, its member exists? Here we seem to have a symmetrical necessary connection between wholly distinct existences. For myself, I agree with David Hume

Logic and feature structures

Abstract: Feature structures play an important role in linguistic knowledge representation in computational linguistics. Given the proliferation of different feature structure formalisms it is useful to have a "common language" to express them in. This paper shows how a variety of feature structures and constraints on them can be expressed in predicate logic (except for the use of circumscription for non-monotonic devices), including sorted feature values, subsumption constraints and the non-monotonic ANY values and "constraint equations". Many feature systems can be completely axiomatized in the Schonfinkel-Bernays class of first-order formulae, so the decidability of the satisfiability and validity problems for these systems follows immediately.

A new formulation of generalized discrete-time time-frequency distributions

Abstract: A definition of generalized discrete-time time-frequency distributions is introduced. This definition utilizes the full information provided by a data sequence so that one can avoid aliasing which is troublesome in the existing definition. The formulation provides a unified framework for implementing Cohen's class of generalized time-frequency distributions which was formulated in the continuous-time domain. Some requirements for the discrete-time kernel in the approach are discussed in association with desirable distribution properties. >

Definition of Reusable Concurrent Software Components

Abstract: In O.O. languages with active objects, a constraint (or behaviour) on method activations is needed to avoid inconsistencies and to meet performance requirements. If the constraint is part of a class definition, the class population grows with the product of the number of behaviours. As pointed out in [Goldsack and Atkinson 1990] this undesirable growth may be controlled by separating the specification of the functional characteristics and the behavioural characteristics of a class. This work extends the concept of behavioural inheritance (b-inheritance) which provides a behaviour to a sequential class. Furthermore, the interaction between b-inheritance and inheritance is discussed. Deontic logic notation for specifying behaviour is extended to deal with the definition of more complex constraints and to improve reusability characteristics of components. The proposal is formalized by extended Petri nets and the translation into a concurrent language is outlined. The project is under development within the O.O. ADA extension DRAGOON [Di Maio et al 1989].

Integrating rules in term subsumption knowledge representation servers

Abstract: This paper addresses the integration of services for rule-based reasoning in knowledge representation servers based on term subsumption languages. As an alternative to previous constructions of rules as concept→concept links. a mechanism is proposed based on intensional roles implementing the axiom of comprehension in set theory. This has the benefit of providing both rules as previously defined. and set aggregation. using a simple mechanism that is of identical computational complexity to that for rules alone. The extensions proposed have been implemented as part of KRS. a knowledge representation server written as a class library in C++. The paper gives an example of their application to the ripple-down rule technique for large-scale knowledge base operation. acquisition and maintenance.

Definitions and Definability

Abstract: Traditionally, the word ‘definition’ means something like explicit definition and, mainly in the philosophy of science, a very limited class of its generalizations. Traditional accounts of definability are often vague and obscure, however, so that it is not always clear what the word stands for. Hence, it is instructive to place definitions in a more formal framework, as we shall see. Such a maneuvre brings forth sophistication which is not practicable in discursive terms — which may sound somewhat paradoxical to philosophers who are accustomed to think of formal methods as yielding intellectual restrictions rather than sophistication. Conversely, there are important pragmatic aspects of definition which cannot be dealt with by using logical tools but rather tools borrowed from the philosophy of language.

Probabilistic Methods in Classification: A Manual for Seven Computer Programs

Abstract: The aim of a general-purpose classification may be expressed as the definition of a set of classes such that class membership is highly predictive of as many attributes as possible Instead of having to describe each object by listing the values of each of its attributes, one aims to encapsulate as much as possible of this description in the simple statement that the object is a member of this or that class

Type Classes are Signatures of Abstract Types

Abstract: We present an extension of Haskell’s type class concept in which a type class is identified with the signature of an abstract type As shown by Mitchell and Plotkin, abstract types can be expressed using existential quantification. Unlike in Mitchell and Plotkin’s work, an abstract type does not come with one — and only one — implementation. Rather, any concrete type can be declared to be an implementation by a clause that corresponds to an instance declaration in Haskell. We introduce F-bounded existential quantification, where an abstract type has the form: $$\exists \alpha .C(\alpha ).\tau (\alpha ).$$ Here, C(α) is a set of constraints that restricts the range of the bound variable α, and τ(α) is a type constructed from α. The expression reads “some type τ(α), where α is some arbitrary fixed type satisfying constraints C(α)”. The constraint set C corresponds to a type class. Just like a type class, it contains declarations for overloaded identifiers as well as conformity clauses that declare one abstract type to be more specific than another.

Particles, pragmatic and other

Abstract: This paper deals with problems in describing, from a synchronic point of view, certain "little words" in Modern Greek like άραγe ("I wonder"), δήθeν ("so-called", "as if"), τάχα ("so-called"), called "hesitation adverbs" by Triantaphyllidis (1978), in his standard grammar of Modern Greek first published in 1941. In previous work I have shown that this class of linguistic items is a rather heterogeneous set from a syntactic, semantic and pragmatic point of view and that not all of them express hesitation on the speaker's part. But if they do not all deserve the name "hesitation adverbs" how else can they be described? At least some of these little words can be (and have been, cf. Tzartzanos 1953) described as particles. However, Zwicky has recently claimed that "languages contain no 'par­ticles' but only words belonging to syntactic categories, clitics, and (inflectional or derivational) affixes” (Zwicky 1985: 294). Moreover, such little words have turned out to play an important role in pragmatic theories, as illocutionary force indicators, discourse markers, etc. Sometimes though, it is not sufficiently clear how the diversity of categories relates to the phenomena described or how the different categories relate to one another. Adequate answers to questions regarding the descriptive level as well as the relations between various descriptive categories used for such twilight zones of language is a necessary prerequisite for evaluating the different theories and the claims of universality with respect to such phenomena.

Discussions Defining the Least Advantaged

Abstract: Some time ago John Rawls published an article entitled ‘A Kantian Conception of Equality’.1 I was struck by Rawls’ change in the definition of the least advantaged class, and have been mildly surprised to see no discussion in the literature about the import of that change. I offer this brief note primarily to publicise the change in Rawls’ views and to invite others to consider the significance of the new definition.

Selection from Overlapping Classifications

Abstract: Semantic classification utilizes structural and semantical properties of data rather than purely their numerical values for constructing classes of objects. In the process of semantic interpretation of data sets, we arrive in our project EXPLORA at a collection of possible descriptions of a given goal set. We propose here a procedure for selecting certain classes from this collection. The procedure chooses them by means of their quality and of a kind of similarity, usually unsymmetric, which we call affinity. The idea is to suppress a class if it is sufficiently similar to, but also inferior to an other class that is itself retained. Some examples illustrate the method and its effect on the results.

Generating good design from bad design: dynamical network approach

Abstract: This paper discusses a dynamical network for mapping of interciass members without performing a learning process. This allows a member of class A to be mapped to a member of class B. Given sample members of each class a backpropagation network is trained to form the corresponding class boundaries. Upon completion of the training process the weights obtained are used in a recurrent network which performs the interclass member mapping without any further training. This mapping is achieved as the recurrent network evolves In time. The Initial state of the network is mapped to its equilibrium state. The interclass member mapping network (IMMN) has many applications in selfcorrecting systems. In this paper the IMMN is developed to represent two classes namely class B (for instance a class for representing members with desirable and correct features) and class A (members with incorrect features). An example is given in which two categories are used namely poorly and well-designed manufacturing parts. Given a poorly-designed part the network wifi suggest corrections resulting in a well-designed part. This example has nonlinear decision regions and shows the generalization capability of the network.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.