Overview

Welcome to Formal Logic: Propositional, Predicate & Modal Logic! This rigorous course offers a comprehensive exploration of theoretical logic principles and proof techniques. You will begin with the foundations of propositional logic, learning how to construct well-formed formulas using atomic propositions and logical connectives. You will delve into semantic interpretation by building truth assignments and designing truth tables to identify tautologies, contradictions, and contingencies.Next, you will master logical equivalences and normal forms. Through clear explanations and step-by-step algorithms, you will learn to apply commutativity, distributivity, De Morgan's laws, and other fundamental equivalence laws to simplify complex formulas and convert them into Conjunctive and Disjunctive Normal Forms.The course then guides you through robust proof systems. You will study natural deduction rules and common inference rules-such as modus ponens, modus tollens, and hypothetical syllogism-to construct structured proofs in propositional logic. You will also explore the soundness and completeness theorems, demonstrating the essential relationship between provable and valid formulas.Building on propositional logic, you will transition to first-order predicate logic. You will define predicates, functions, variables, and quantifiers (universal and existential), and learn how to interpret first-order languages over domains and assignments. You will tackle the intricacies of scope, free and bound variables, and logical properties that govern quantified formulas.You will practice translating natural language statements into precise first-order formulas, resolving scope ambiguities and nested quantifiers. Through guided examples, you will develop the skills to formalize everyday and philosophical assertions in logical notation. You will also apply natural deduction techniques with quantifier introduction and elimination rules, and explore identity, equality axioms, and their substitutive properties in proofs.In the final module, you will study modal logic and Kripke semantics. You will examine necessity and possibility operators, define accessibility relations in possible-world models, and analyze axiomatic systems such as K, T, S4, and S5. You will learn proof methods including modal sequent calculus and labeled deduction, and explore correspondence theory to connect modal axioms with frame conditions.The course concludes with an overview of advanced topics-undecidability results, Löwenheim-Skolem theorems, and modal logic extensions (temporal, deontic, epistemic). You will discover practical applications in computer science, linguistics, and philosophy, and receive guidance on next steps for further study.Throughout this course, you will engage with detailed lectures, worked examples, and challenging exercises to solidify your understanding. By the end, you will possess a strong theoretical foundation in propositional, predicate, and modal logic, ready to apply formal reasoning in research, software verification, or advanced academic study.

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