Logika Matematika – Mathematical Logic
Deskripsi Mata Kuliah – Course Description:
Mata kuliah ini memberikan paparan rinci mengenai logika matematika untuk ilmu komputer. Ada lima topik utama pada kuliah ini, yaitu: logika proposisi, logika predikat orde pertama, metode pembuktian matematis, induksi matematika, dan teori himpunan elementer. Topik-topik ini dikelompokkan ke dalam empat capaian pembelajaran (Course Learning Outcome, CLO), yaitu: CLO 1 (logika proposisi), CLO 2 (logika predikat orde pertama), CLO 3 (metode pembuktian matematis dan induksi matematika), dan CLO 4 (teori himpunan elementer). Materi terkait logika proposisi meliputi: nilai kebenaran dari formula proposisional, konversi dari bahasa alami ke formula proposisional, dan inferensi untuk kalkulus proposisi. Untuk topik logika predikat, materi yang dibahas adalah: interpretasi dan nilai kebenaran formula predikat sederhana, konversi dari bahasa alami ke formula predikat, inferensi untuk kalkulus predikat, dan pengenalan Prolog sebagai bahasa deklaratif berbasis logika. Mahasiswa juga akan mempelajari metode pembuktian elementer dan dua tipe induksi matematika (induksi matematika biasa dan induksi kuat). Topik terakhir adalah teori himpunan elementer, yang meliputi definisi dan notasi himpunan, relasi elementer antar himpunan, dasar-dasar operasi himpunan, dan prinsip inklusi-eksklusi.
Mathematical Logic A course provides a rigorous exposure concerning mathematical logic for computer science. There are five main topics in this course, i.e.: propositional logic, first-order predicate logic, mathematical proof methods, mathematical induction, and elementary set theory. These topics are grouped into four course learning outcomes (CLO), namely: CLO 1 (propositional logic), CLO 2 (first-order predicate logic), CLO 3 (mathematical proof methods and mathematical induction), and CLO 4 (elementary set theory). The materials relating to propositional logic include: truth value of a propositional formula, conversion of natural language sentences to propositional formulas, and inference methods for propositional calculus. For predicate logic topic, the materials include: interpretation and truth of simple predicate formulas, conversion of natural language sentences to predicate formulas, inference method for predicate calculus, and introduction to Prolog as a declarativelogic programming framework. The students will also learn elementary mathematical proof methods and two elementary types of mathematical induction (the ordinary mathematical induction and the strong induction).The final topic of the course is elementary set theory, which covers set definition and notation, elementary set relation, basic set operations, and inclusion-exclusion principle.
Pustaka – Bibliography:
Utama:
1. K. H. Rosen, Discrete Mathematics and Its Applications, 8th Edition.
McGraw-Hill, 2019
Pendukung:
1. S. S. Epp. Discrete Mathematics with Applications, 5th Edition. Brooks/
Cole Cengage Learning, 2018.
2. M. Huth and M. Ryan, Logic in Computer Science: Modelling and
Reasoning about Systems (Chapter 1 and 2), 2nd Edition, 2004.
3. M. Bramer, Logic Programming with Prolog (Chapter 1 and 2), 2nd Edition,
Springer, 2013.
4. M. Ben-Ari, Mathematical Logic for Computer Science (Chapter 1,2,3,5,8),
2nd Edition, 2000.
5. H. J. Gensler, Introduction to Logic, Routledge, New York, 2010.
6. V. Klenk, Understanding Symbolic Logic, Pearson Prentice Hall, 2008.
7. R. Munir, Matematika Diskrit (5th edition [revised]), Informatika, 2012.
