The Standard Aspect of Dialectical Logic

TL;DR

This paper introduces the standard aspect of dialectical logic, emphasizing its dynamic nature and its ability to unify small-scale and large-scale programming through a novel semantic framework.

Contribution

It defines the standard aspect of dialectical logic using local cartesian closure, extending traditional semantics with a unified dynamic logical framework.

Findings

Provides a natural program semantics incorporating Hoare's semantics

Extends Kripke semantics for dynamic logic

Unifies small-scale and large-scale programming logic

Abstract

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed by the notions of process and flow in dialectical logic. Dialectical logic has a standard aspect, which can be defined in terms of the "local cartesian closure" of subtypes. The standard aspect of dialectical logic provides a natural program semantics which incorporates Hoare's precondition/postcondition semantics and extends the standard Kripke semantics of dynamic logic. The goal of the standard aspect of dialectical logic is to unify the logic of small-scale and large-scale programming.