--- title: Modal Logic description: Modal logic extends classical logic to represent statements about necessity, possibility, belief, and time. You will understand how to use modal operators, construct Kripke semantics, and apply these formalisms to computer science, philosophy, and artificial intelligence. category: mathematics subcategory: mathematical-logic difficulty: beginner, intermediate, advanced url: /subject/modal-logic --- # Modal Logic Modal logic extends classical logic to represent statements about necessity, possibility, belief, and time. You will understand how to use modal operators, construct Kripke semantics, and apply these formalisms to computer science, philosophy, and artificial intelligence. ## Available Resources 3 Books • 2 Courses • 3 Websites ## Websites ### 1. Stanford Encyclopedia of Philosophy: Modal Logic James Garson's encyclopedia entry surveys modal logic from the basic system K through T, S4 and S5, possible-worlds semantics, frame conditions, quantified modal logic, and deontic, temporal and conditional variants. Readers gain a map of the core systems and how they relate. **Difficulty:** Beginner | **Price:** Free **Link:** https://plato.stanford.edu/entries/logic-modal/ **Tags:** modal-logic, possible-worlds-semantics, kripke-frames, normal-modal-logics, quantified-modal-logic ### 2. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 3. plato.stanford.edu The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://plato.stanford.edu **Tags:** websites, mathematics-statistics, discrete-math ## Courses ### 1. Modal Logic Learn modal logic with this comprehensive course by Wesley H. Holliday! Explore the fundamentals and applications of modal-logic. **Difficulty:** Advanced | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLXKKIUdnOESGk43pUg3NTkRWjglvKXKi7 ### 2. Logic for Computer Science A Coursera course from BITS Pilani on computational logic: propositional and predicate logic, natural deduction, soundness and completeness, undecidability, LTL and CTL model checking, and Floyd-Hoare program verification. Learners can write formal proofs and verify properties of algorithms and systems. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/bits-logic-for-computer-science **Tags:** propositional-logic, predicate-logic, model-checking, temporal-logic, hoare-logic, program-verification ## Books ### 1. Modal Logic: An Introduction **Author:** Brian F. Chellas A Cambridge textbook developing propositional modal logic systematically: standard and minimal (neighbourhood) models, normal and classical systems, soundness, completeness, decidability and filtration, with many exercises. Readers learn to prove metatheorems for modal systems and follow the technical literature. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0521295157?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematical-logic ### 2. Modal Logic **Author:** Patrick Blackburn, Maarten de Rijke, Yde Venema A graduate textbook from the Cambridge Tracts in Theoretical Computer Science treating modal languages as tools for describing relational structures. Covers bisimulation, frame definability, canonical models, completeness, the finite model property, algebraic semantics and complexity, preparing readers for research-level work. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0521527147?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematical-logic ### 3. Introduction to Modal Logic **Author:** G. E. Hughes, M. J. Cresswell The classic 1968 textbook introducing propositional and quantified modal logic, including the systems T, S4 and S5, decision procedures and possible-worlds semantics. Readers learn to construct proofs and assess validity in standard modal systems. Later superseded by the authors' New Introduction. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/041629460X?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematical-logic --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/modal-logic