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Chapter 1: Philosophical Motivation 417 §1.1: Introduction 417 §1.2: Temporal Dualism 418 Chapter 2: The Prepositional Logic I 420 §2.1: Formal Language LI 420 §2.2: Semantics for I 421 §2.3: Dl-sequence 423 §2.4: Formal System I 425 §2.5: The Soundness and Completeness of I 427 Chapter 3: The Prepositional Logic IM 435 §3.1: Formal Language LIM 435 §3.2: Semantics for IM 436 §3.3: DMI-sequence and DIM-sequence 441 §3.4: Formal System IM 445 §3.5: The Soundness and Completeness of IM 450 Chapter 4: Some Applications 450 § 4.1: Some Interesting Tense Operators Definable within IM 450 §4.2: Tense and Aspect within IM 455

Interval logics with applications to study of tense and aspect in English