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2 International Journal of Applied Mathematics and Computer Science

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On some properties of grounding nonuniform sets of modal conjunctions

Katarzyniak R. P.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 3

399-412

A language grounding problem is considered for nonuniform sets of modal conjunctions consisting of conjunctions extended with more than one modal operator of knowledge, belief or possibility. The grounding is considered in the context of semiotic triangles built from language symbols, communicative cognitive agents and external objects. The communicative cognitive agents are assumed to be able to observe external worlds and store the results of observations in internal knowledge bases. It is assumed that the only meaning accessible to these agents and assigned to modal conjunctions can be extracted from these internal knowledge bases. Commonsense requirements are discussed for the phenomenon of grounding nonuniform sets of modal conjunctions and confronted with an original idea of epistemic satisfaction relation used to define proper conditions for language grounding. Theorems are formulated and proved to show that the communicative cognitive agents based on the proposed model of grounding fulfill some commonsense requirements given for processing sets of nonuniform modal conjunctions. The main result is that the communicative cognitive agents considered can be constructed in a way that makes them rational and intentional as regards the processing of modal conjunctions and from the human point of view.

Grounding and extracting modal responses in cognitive agents: 'AND' query and states of incomplete knowledge

Katarzyniak R. P., Pieczyńska-Kuchtiak A.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 2

249-263

In this study an original way of modeling language grounding and generation for a simple set of language responses is presented. It is assumed that the language is used by a cognitive agent and consists of a few modal belief and possibility formulas that are used by this agent to communicate its opinions on the current state of an object. The cognitive agent is asked a simple AND query and the language is tailored to this situation. The agent's knowledge bases are characterized by certain incompleteness of information on the current state of objects. The language of the available responses is originally grounded in the agent's previous empirical experience. According to the assumptions of the cognitive linguistics and the phenomenology of knowledge, this experience is the basic source of meaning represented by the available formulas (responses). In the study the idea of an epistemic satisfaction relation is introduced that describes states of the agent's knowledge in which particular formulas are satisfied in the epistemic sense. Additionally, a formal description of the semantic power of formulas is presented. The concepts of the empirical satisfaction relation and the semantic power of formulas are used to define a model of particular language behavior that preserves the assumption of language grounding. Two examples of possible implementations are given. These implementations are basic ones and refer to statistical characteristics of the stored empirical experience of the cognitive agent.