There is a gap between two different modes of computation: the symbolic mode and the subsymbolic (neuron-like) mode. The aim of this paper is to overcome this gap by viewing symbolism as a high-level description of the properties of (a class of) neural networks. Combining methods of algebraic semantics and non-monotonic logic, the possibility of integrating both modes of viewing cognition is demonstrated. The main results are (a) that certain activities of connectionist networks can be interpreted as non-monotonic inferences, and (...) (b) that there is a strict correspondence between the coding of knowledge in Hopfield networks and the knowledge representation in weight-annotated Poole systems. These results show the usefulness of non-monotonic logic as a descriptive and analytic tool for analyzing emerging properties of connectionist networks. Assuming an exponential development of the weight function, the present account relates to optimality theory – a general framework that aims to integrate insights from symbolism and connectionism. The paper concludes with some speculations about extending the present ideas. (shrink)

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a (...) set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language. (shrink)

Argumentation has been an important topic in knowledge representation, reasoning and multi-agent systems during the last twenty years. In this paper, we propose a new abstract framework where arguments are associated with a strength, namely a quantitative information which is used to determine whether an attack between arguments succeeds or not. Our Strength-based Argumentation Framework combines ideas of Preference-based and Weighted Argumentation Frameworks in an original way, which permits to define acceptability semantics sensitive to the existence of accruals between arguments. (...) The question of accruals arises in situations where several arguments defending the same position against another argument are unable to individually defeat this argument, but could do it collectively if they combine their strengths. We investigate some of the theoretical and computational properties of our new framework and semantics, and present a reasoning algorithm that is based on a translation of the problem into pseudo-boolean constraint satisfaction. This paper proposes an intuitive framework which allows strength compensations in an argumentation context where attacks may not succeed, completed by an approach which detects accruals throughout the reasoning process without requiring the elicitation of all compensatory combinations of arguments as an input. (shrink)

We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on (...) the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule- based reasoning and whether they involve distributed or localist representations. The bene®ts and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used (...) for cognitive modelling. q 2001 Elsevier Science Ltd. All rights reserved. (shrink)