Vector logic¶

An algebraic representation of logical truth values and connectives as vectors and matrices acting on a finite-dimensional space.

Version: v1 · 2026-09-08 · History
Domain-specific #: 7400
Origin domain: mathematical logic and computing
Subdomain: mathematical logic and computing

Core Idea¶

Different vector-logic systems encode Boolean, many-valued, fuzzy or predicate logic and can use tensor products for compound propositions; representation choices determine whether operations preserve classical truth tables. Truth values are mapped to basis or state vectors, logical connectives become linear or multilinear operators and composition of matrices evaluates complex formulas in the encoded space. 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¶

Vector logic belongs to mathematical logic and computing and is useful where the analyst can specify the typed mathematical logic and computing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the logical system and truth values, vector space and basis encoding, matrix or tensor operators for each connective, composition rule, normalization and proof of truth-table or semantic correspondence are explicit. The scope is broad within that domain but bounded by the need for the logical system and truth values, vector space and basis encoding, matrix or tensor operators for each connective, composition rule, normalization and proof of truth-table or semantic correspondence are explicit.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the logical system and truth values, vector space and basis encoding, matrix or tensor operators for each connective, composition rule, normalization and proof of truth-table or semantic correspondence 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 Vector logic. Vector 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 mathematical logic and computing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the logical system and truth values, vector space and basis encoding, matrix or tensor operators for each connective, composition rule, normalization and proof of truth-table or semantic correspondence are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of mathematical logic and computing because they reuse the typed mathematical logic and computing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Truth values are mapped to basis or state vectors, logical connectives become linear or multilinear operators and composition of matrices evaluates complex formulas in the encoded space., and type the carrier, state every parameter and convention in the definition, test that the logical system and truth values, vector space and basis encoding, matrix or tensor operators for each connective, composition rule, normalization and proof of truth-table or semantic correspondence are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Vector logic Domain-specific

Parents (1) — more general patterns this builds on

Vector logic is a kind of Representation Prime

The proposed strict upward parent is prime:representation.

Hierarchy path (1) — routes to 1 parentless root

Vector logic → Representation → Abstraction

Neighborhood in Abstraction Space¶

Vector logic sits in a crowded region of the domain-specific corpus (10^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Formal Logic & Type Theory (34 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08