MATHEMATICAL LOGIC AND PROBABILITY MODELS IN BUILDING EXPLAINABLE ARTIFICIAL INTELLIGENCE FOR DIGITAL ENTERPRISES

Explainable artificial intelligence has become essential for building trust in digital enterprises, especially in fragile contexts like Iraq between 2020 and 2024. This study assessed how mathematical logic and probability models shaped explainability outcomes, including transparency, traceability, trust, and adoption. A descriptive design relying on 25 sector-year observations from secondary sources guided the analysis. Correlation results showed strong positive links between explainability outcomes and explanation techniques at 0.80, symbolic logic at 0.77, and probabilistic modeling at 0.73, while contextual conditions had a negative effect at −0.58. Regression confirmed explanation techniques as the strongest driver with a coefficient of 0.36, followed by symbolic logic at 0.27 and probabilistic modeling at 0.23, while contextual conditions reduced outcomes at −0.19. The model explained 79 percent of the variance, validating the predictive strength of the framework. Findings revealed that dashboards, Bayesian networks, and post-hoc explainers improved transparency indexes from 30 to 50, trust scores from 30 to 50, and adoption rates from 5 to 14 percent across enterprises. The results imply that explainable AI can improve accountability and competitiveness, but weak infrastructure and low literacy remain major constraints. Recommendations urge policymakers to invest in digital readiness, managers to expand logic and probability models beyond pilots, and educators to embed explainable AI training in curricula.