Scales and Hedges in a Logic with Analogous Semantics

TL;DR

This paper introduces a novel logical framework combining analogous semantics with a two-layered logic system, addressing complex formula formation and reasoning, with applications in cognitive and social decision-making.

Contribution

It extends the Context Logic (CL) to handle scales for adjective and verb semantics, integrating it with the Activation Bit Vector Machine for improved reasoning.

Findings

Handles complex formulae formation and grounding.

Integrates scales for adjective and verb semantics.

Provides a reasoning mechanism based on VSA model.

Abstract

Logics with analogous semantics, such as Fuzzy Logic, have a number of explanatory and application advantages, the most well-known being the ability to help experts develop control systems. From a cognitive systems perspective, such languages also have the advantage of being grounded in perception. For social decision making in humans, it is vital that logical conclusions about others (cognitive empathy) are grounded in empathic emotion (affective empathy). Classical Fuzzy Logic, however, has several disadvantages: it is not obvious how complex formulae, e.g., the description of events in a text, can be (a) formed, (b) grounded, and (c) used in logical reasoning. The two-layered Context Logic (CL) was designed to address these issue. Formally based on a lattice semantics, like classical Fuzzy Logic, CL also features an analogous semantics for complex fomulae. With the Activation Bit Vector Machine (ABVM), it has a simple and classical logical reasoning mechanism with an inherent imagery process based on the Vector Symbolic Architecture (VSA) model of distributed neuronal processing. This paper adds to the existing theory how scales, as necessary for adjective and verb semantics can be handled by the system.