LOGICAL AND PSYCHOLOGICAL PARTITIONING OF MIND: DEPICTING THE SAME MAP?

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. In the sake of this aim, the paper first summarizes Demetriou's theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypecognitive system that monitors and controls the functioning of all other systems. In the second part the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed in the concluding part of the paper

Syntactic Computation as Labelled Deduction: WH a case study

This paper addresses the question "Why do WH phenomena occur with the particular cluster of properties observed across languages -- long-distance dependencies, WH-in situ, partial movement constructions, reconstruction, crossover etc." These phenomena have been analysed by invoking a number of discrete principles and categories, but have so far resisted a unified treatment. The explanation proposed is set within a model of natural language understanding in context, where the task of understanding is taken to be the incremental building of a structure over which the semantic content is defined. The formal model is a composite of a labelled type-deduction system, a modal tree logic, and a set of rules for describing the process of interpreting the string as a set of transition states. A dynamic concept of syntax results, in which in addition to an output structure associated with each string (analogous to the level of LF), there is in addition an explicit meta-level description of the process whereby this incremental process takes place. This paper argues that WH-related phenomena can be unified by adopting this dynamic perspective. The main focus of the paper is on WH-initial structures, WH in situ structures, partial movement phenomena, and crossover phenomena. In each case, an analysis is proposed which emerges from the general characterisatioan of WH structures without construction-specific stipulation.Articl

Doing and Showing

The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a mathematical theory consists of a set of axioms and further theorems deduced from these axioms according to certain rules of logical inference. Thus the usual notion of axiomatic method is inadequate and needs a replacement.Comment: 54 pages, 2 figure

A Formal Context Representation Framework for Network-Enabled Cognition

Network-accessible resources are inherently contextual with respect to the specific situations (e.g., location and default assumptions) in which they are used. Therefore, the explicit conceptualization and representation of contexts is required to address a number of problems in Network- Enabled Cognition (NEC). We propose a context representation framework to address the computational specification of contexts. Our focus is on developing a formal model of context for the unambiguous and effective delivery of data and knowledge, in particular, for enabling forms of automated inference that address contextual differences between agents in a distributed network environment. We identify several components for the conceptualization of contexts within the context representation framework. These include jurisdictions (which can be used to interpret contextual data), semantic assumptions (which highlight the meaning of data), provenance information and inter-context relationships. Finally, we demonstrate the application of the context representation framework in a collaborative military coalition planning scenario. We show how the framework can be used to support the representation of plan-relevant contextual information

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way that the strengths of either paradigm will be retained. Current state-of-the-art research, however, fails by far to achieve this ultimate goal. As one of the main obstacles to be overcome we perceive the question how symbolic knowledge can be encoded by means of connectionist systems: Satisfactory answers to this will naturally lead the way to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page