# From Knowledge to Conjectures: A Modal Framework for Reasoning about Hypotheses

arXiv: https://arxiv.org/abs/2508.07304 · HTML: https://mlsanity.com/paper/2508.07304/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 53 references that are in the map.
- First posted on arXiv 10 Aug 2025.

## Builds on (most cited first, 2 of 2)

- [A modal logic amalgam of classical and intuitionistic propositional logic](https://mlsanity.com/paper/1306.2068/) (2013)
- [Intuitionistic Non-Normal Modal Logics: A general framework](https://mlsanity.com/paper/1901.09812/) (2019)

## Built on by (most cited first, 1 of 1)

- [Provenance-Enhanced Statements in Knowledge Graphs](https://mlsanity.com/paper/2606.15246/) (2026)

## Abstract (arXiv)

This paper introduces a new family of cognitive modal logics designed to formalize conjectural reasoning: modal systems in which cognitive contexts extend known facts with hypothetical assumptions in order to explore their consequences. Unlike traditional doxastic and epistemic systems, conjectural logics rely on a principle, called Axiom C (varphi rightarrow Boxvarphi), through which established facts are preserved across conjectural layers. While Axiom C has often been treated with suspicion because of its association with modal collapse, we show that collapse does not arise from C alone, but requires either the presence of Axiom T or a concretely bivalent base logic. Accordingly, we avoid T and adopt a non-bivalent semantic framework, such as supervaluation-style semantics, Weak Kleene logic, or Description Logic, in which undefined propositions may coexist with modal assertions. This prevents modal collapse and preserves a distinction between factual and conjectural statements. Within this framework we define the modal systems KC and KDC, show that Axiom C directly implies 4 and 5, and prove that these systems are non-trivial, sound, and complete. An inclusion theorem links reality, doxastic states, epistemic states, and conjectural states via set-theoretic inclusion among valuations, providing a unified account of how these layers relate. Finally, we introduce a dynamic operator, mathsfsettle(p), which formalizes the transition by which a conjectural extension becomes designated reality, thereby motivating a corresponding Conjectural Dynamic Logic.