Logikarrays

Logikarrays is a hypothetical data structure used in theoretical computer science to combine grid storage with logical inference. They store truth-valued information in an array-like form while supporting efficient application of logical operations.

Structure and semantics: A logikarray is an n-dimensional array whose elements belong to a logic domain (for example boolean, ternary, or probabilistic values). Dimensions index variables or attributes, and predicate-based indexing selects subarrays. Element-wise logical operators, as well as reductions representing exists and for all, enable compact expression of logical formulas.

Operations: Basic operations include and, or, not, and XOR; relational operators and implications can be implemented from these primitives. Reductions compute global truth values, while filters select elements by predicates; mapping applies functions element-by-element.

Implementation considerations: Dense versus sparse representations, handling unknown values, memory layout, and cache efficiency matter for performance. Parallelism, including SIMD or GPU acceleration, is often explored. Integrating with logic programming tools is a common design goal.

Applications: Logikarrays appear in theoretical studies of symbolic AI, model checking, knowledge representation, and database querying with logical predicates. They offer a bridge between array programming and logic programming, enabling concise expressions of global properties over large data sets.

Example: A 2×3 logikarray with boolean values can encode the truth status of a binary relation across a small domain; a global all operation can test whether the relation holds universally.