A Note on Nonemptiness of Cognitive Semantics for Linguistic Representations of Modal Equivalence

Abstract

In this paper we deal with an original model of technically oriented cognitive semantics of modal equivalences, stated in semi-controlled natural languages and used as surface linguistic representations of internal knowledge states of artificial autonomous systems. The cognitive semantics is defined to support generation of natural language statements extended with auto-epistemic operators of modality, representing subjectively experienced certainty, strong belief and week belief of the autonomous system that the relationship between occurrence of two chosen properties in a real object is the logical equivalence relation. An internal architecture of the autonomous system is briefly presented with particular emphasis on computational modules responsible for verification of compliance of current knowledge processing states with states described by the cognitive semantics as proper for application of a particular case of modal equivalence. The major issue discussed in the paper concerns an original theory of grounding of modal equivalences in empirical knowledge resources, encapsulated in the autonomous system. The whole theory consists of theorems describing basic and advanced properties of the cognitive semantics. In the paper, the attention is limited to presentation and proof of four theorems about nonemptiness of the proposed cognitive semantics. The research results cover the next stage of some research and development efforts, concerning the technical implementation of cognitive computing models, describing the artificial generation of semi-natural languages by the interactive autonomous system to describe their encapsulated knowledge resources.

Implementing Cognitive Semantics of Autoepistemic Membership Statements: The Case of Categories with Prototypes

“…The presented model of cognitive semantics, tailored to categories with a prototype, substantially extends previous results for categories without a prototype [18][19][20][21][22][23][24][25][26][27]. It has been proven that the proposed cognitive semantics have properties necessary to conform to human linguistic behavior.…”

“…Probably one of the most interesting features of our proposed method of introducing computational mechanisms for the production of autoepistemic membership statements is the resulting possibility of carrying out analytical verification of the features of this process, when already at the stage of determining the agent's architecture and adopting specific definitions of cognitive semantics. Indeed, this possibility was already used to handle autoepistemic membership statements communicating beliefs about the belonging of objects to categories without a prototype [18][19][20][21]26,27]. Below we present, in our opinion, the most important features of our proposed extended cognitive semantics mechanism, emphasizing at the same time that the list of theorems given below should be considered together with the theorems formulated, among others, in work [18].…”

“…Some introductory studies into the cognitive semantics of autoepistemic implications Σ(x ∈ p ⇒ x ∈ q) were proposed in [24,25]. Works [26,27] on modal equivalences Σ(x ∈ p ⇔ x ∈ q) for categories without prototypes covered an additional aspect of the obligatory verification of the scope of processing of the collected empirical experience by the agent, and in particular the experience determining whether objects belong to a category. The feasibility of the approach has been shown both through analytical proofs and using simulations.…”

“…The main goal of this article was to propose and sufficiently describe a substantial extension of the original model presented in the series of papers [18][19][20][21][22][23][24][25][26][27] by adding mechanisms for handling categories with prototypes. Therefore, the presentation concentrates only on the proposed extensions of the agent's architecture and the related reformulations of original cognitive semantics.…”

“…It follows directly fromDefinition 13, where the conditions of the epistemic satisfaction relation are the same for both formulas.The general conclusion resulting from the list of theorems formulated above, supplemented by the theorems discussed in work[18], is that the design and implementation of an artificial cognitive agent as is described by the proposed theory (including specific definitions of cognitive semantics) makes it possible to realize an intelligent interactive system generating linguistic behavior consistent with human linguistic behavior, at least in terms of processing autoepistemic membership statements communicating beliefs about the belonging of observed objects to a category with a prototype. After taking into account the results presented in works[19][20][21][22][23][24][25][26][27] (some of which also presented simulation studies),…”