Integration of Interval Temporal Logic in an Expression Evaluator

This paper presents NAXE, an expression evaluator framework for concurrent, resilient, and temporally aware applications, particularly in IoT domains. The key contribution is the principled integration of Interval Temporal Logic as a first-class feature alongside standard arithmetic and Boolean operations. To enhance robustness, bidirectional lazy evaluation extends short-circuit semantics to yield determinate results even with indeterminate operands. A left-to-right chaining syntax and Quantified Expressions reduce cognitive load and improve accessibility, particularly for non-programmers. The framework’s asynchronous evaluation model uses callbacks over an Abstract Syntax Tree with formal operational semantics specified through EBNF. Validation combines (i) formal correctness proofs, (ii) empirical validation (over 300 unit tests), (iii) real-world deployment in a hotel IoT system and (iv) a pilot study (n = 36). This integration advances expression evaluation by supporting interval-temporal operators, determinate outcomes under indeterminate operands, quantifiers and user-oriented syntax in a single expression-evaluation design.