Anti-Goal Reasoning: Rethinking the Theory of Goal Reasoning in Non-Axiomatic Logic

2026-07-22

AI Summary

This work addresses a longstanding issue in Non-Axiomatic Logic (NAL), where the conventional formalization of “avoid G” as “¬G!” leads to semantic ambiguities and reasoning paradoxes. To resolve this, the paper introduces a novel goal-reasoning mechanism that explicitly defines the notion of an “anti-goal” within the NAL framework and incorporates a new mental operator, *prevent*, to rigorously distinguish among four distinct behavioral intentions: pursuing, passively avoiding, actively preventing, and maintaining the status quo. Through four minimal case studies, the proposed approach effectively eliminates the logical inconsistencies arising from the traditional representation and enables precise modeling and reasoning about avoidance-oriented goals.

Abstract

Goal reasoning in Non-Axiomatic Logic (NAL) explains how an adaptive system derives means for realizing desired events under insufficient knowledge and resources. However, the representation of avoidance is less clear. A common convention is to express ``avoid $G$'' as the goal sentence ``$\neg G!$'', but this notation conflates two different readings: pursuing the negated event $\neg G$, and avoiding the positive event $G$. This paper shows that the conflation can produce a paradoxical case in which an avoidance intention is converted into a positive goal to act merely because acting is usually followed by the absence of hurt. Starting from NAL's basic definition of goals, the framework is extended with a corresponding definition of anti-goals, so that avoidance can be represented without treating it as the pursuit of a negated event. Finally, a mental operation, $\op{prevent}$, is introduced to connect anti-goal reasoning with ordinary goal reasoning in cases of active prevention. Four minimal case studies check that the resulting rules distinguish pursuit, passive avoidance, active prevention, and withholding action to preserve a desired event.

Problem

• Goal reasoning
• Non-Axiomatic Logic
• Avoidance
• Anti-goal
• Representation ambiguity

Innovation

• anti-goal reasoning
• Non-Axiomatic Logic
• goal representation
• avoidance modeling
• prevent operation