Hyperintensional Intention
Daniil Khaitovich, Aybüke Özgün
TL;DR
The paper addresses the problem that traditional logics of intention enforce closure principles that lead to undesirable side-effects. It develops a hyperintensional logic that ties intentions to decision problems modeled as atomic objects within a problem-sensitive, bi-modal framework. A complete axiomatization is provided, and the semantics demonstrate how locking onto decision problems yields valid principles like consistency and agglomeration while avoiding closure under equivalence. The framework offers a principled tool for analyzing rational intention and deliberation, with avenues for future work including belief interplay, control, nesting, dynamics, and multi-agent extensions.
Abstract
Intentions are crucial for our practical reasoning. The rational intention obeys some simple logical principles, such as agglomeration and consistency, among others, motivating the search for a proper logic of intention. However, such a logic should be weak enough not to force the closure under entailment; otherwise, we cannot distinguish between intended consequences of agents' choices and their unintended side-effects. In this paper we argue that we should avoid not only the closure under entailment, but the weaker closure under equivalence as well. To achieve this, we develop a hyperintensional logic of intention, where what an agent intends is constrained by the agent's decision problem. The proposed system combines some elements of inquisitive and topic-sensitive theories of intensional modals. Along the way, we also show that the existing closest relatives of our framework overgenerate validities by validating some instances of closure under equivalence. Finally, we provide a sound and strongly complete axiomatization for this logic.