Doxastic logic¶
A modal logic that formalizes what agents believe and how those beliefs interact with implication, introspection and consistency.
Core Idea¶
Belief is weaker than knowledge and need not be true, different axiom systems model idealized agents differently and logical omniscience is a modeling limitation. A belief operator indexed by an agent is interpreted over accessible possible worlds; frame conditions validate axioms governing closure, consistency and positive or negative introspection. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Doxastic logic belongs to philosophical logic and is useful where the analyst can specify the typed philosophical logic carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the agents and proposition language, indexed belief modalities, Kripke worlds and accessibility relation, truth clause for belief, selected normality consistency and introspection axioms, frame correspondences, belief revision or multi-agent extensions and distinction from epistemic logic are explicit. The scope is broad within that domain but bounded by the need for the agents and proposition language, indexed belief modalities, Kripke worlds and accessibility relation, truth clause for belief, selected normality consistency and introspection axioms, frame correspondences, belief revision or multi-agent extensions and distinction from epistemic logic are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the agents and proposition language, indexed belief modalities, Kripke worlds and accessibility relation, truth clause for belief, selected normality consistency and introspection axioms, frame correspondences, belief revision or multi-agent extensions and distinction from epistemic logic are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Doxastic logic. Doxastic logic compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed philosophical logic carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the agents and proposition language, indexed belief modalities, Kripke worlds and accessibility relation, truth clause for belief, selected normality consistency and introspection axioms, frame correspondences, belief revision or multi-agent extensions and distinction from epistemic logic are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of philosophical logic because they reuse the typed philosophical logic carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, A belief operator indexed by an agent is interpreted over accessible possible worlds; frame conditions validate axioms governing closure, consistency and positive or negative introspection., and type the carrier, state every parameter and convention in the definition, test that the agents and proposition language, indexed belief modalities, Kripke worlds and accessibility relation, truth clause for belief, selected normality consistency and introspection axioms, frame correspondences, belief revision or multi-agent extensions and distinction from epistemic logic are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Doxastic logic Domain-specific
Parents (1) — more general patterns this builds on
-
Doxastic logic is a kind of Belief Formation Prime
The proposed strict upward parent is
prime:belief_formation.
Hierarchy path (1) — routes to 1 parentless root
- Doxastic logic → Belief Formation → Interpretation → Representation → Abstraction
Neighborhood in Abstraction Space¶
Doxastic logic sits in a crowded region of the domain-specific corpus (7th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Truth, Semantics & Logical Systems (18 abstractions)
Nearest neighbors
- Relevance logic — 0.94
- T-schema — 0.93
- Semantic theory of truth — 0.93
- Radical probabilism — 0.93
- Proof-theoretic semantics — 0.92
Computed from structural-signature embeddings · 2026-09-08