Propositional Logic Syntax Semantics and Truth Tables

Lecture 17 of CS607 Artificial Intelligence establishes the mathematical rigor of formal logic as a foundational language for knowledge representation and reasoning. The lecture begins with Propositional Logic (Boolean Logic), examining its formal Syntax and Semantics. An atomic proposition is an assertive declarative statement that can be either True or False. Students study formal logical connectives: Negation (NOT), Conjunction (AND), Disjunction (OR), Implication (IF-THEN, with truth table demonstrating that false premises trivially imply anything), and Biconditional (IF-AND-ONLY-IF). Truth Tables are analyzed as a deterministic semantic evaluation mechanism to classify logical sentences into Tautologies (sentences that are true under all possible world interpretations), Contradictions (sentences that are false under all interpretations), and Contingencies. The formal concept of Logical Entailment (alpha |= beta) is introduced. Computer vision methodologies spanning edge detection, feature extraction, and image segmentation are evaluated alongside robotic kinematic architectures. Unsupervised clustering algorithms such as k-means are examined to discover latent taxonomic groupings within unlabelled multidimensional datasets. Minimax game tree evaluations demonstrate how optimal zero-sum strategies are determined in competitive two-player adversarial environments. Alpha-beta pruning mathematical cutoffs are analyzed, proving that identical game decisions are reached with significantly fewer evaluated board states. By engaging with solved past papers by Moaaz and Waqar Siddhu, learners gain actionable insights into recurrent university exam questions. Interactive quiz assessments on VU SIGMA facilitate rapid knowledge verification and retention of critical artificial intelligence terminology. Comprehensive coverage of IEEE and AAAI standards ensures learners communicate with technical precision across global computational intelligence organizations. Detailed analysis of semantic networks and frame systems illustrates how hierarchical inheritance models capture structured real-world domain knowledge. The strategic role of expert system shells is evaluated as an instrument for decoupling domain knowledge bases from generic inference engines. Certainty factor calculi and probabilistic reasoning provide systematic mechanisms for managing incomplete and noisy real-world evidentiary data. The culminating synthesis highlights emerging frontiers in autonomous systems, deep learning architectures, and ethical artificial intelligence governance.