Core – MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
To know about Mathematical techniques required for computer science.
Unit I Hrs 18
Statements and Notation – Connectives – Negation – Conjunction – Disjunction - Statements formulas and Truth tables-Conditional and Biconditional - Well formed formulas – Tautologies -Equivalence of formulas - Duality law - Tautological Implications - Formulas with Distinct Truth tables.
Unit II Hrs 18
Two state devices and statement logic-Disjunctive Normal Forms-Conjunctive normal forms-Principal Disjunctive normal forms-Principal Conjunctive Normal forms -Rules of inference-Consistency of premises and indirect method of proof-Theory of inference for the predicate calculas.
Unit III Hrs 18
Matrices - Various types of matrices - Operations on matrices - Multiplication of matrices -Adjoint and Inverse of a matrices - Characteristic roots and Characteristic Equation of a matrices.
Unit IV Hrs 18
An Introduction to Description Logics-From networks to Description Logics-Knowledge representation in Description Logics- Description Logics systems - Applications developed with Description Logics systems-Relationship to other fields of Computer Science - Basic Description Logics- Introduction -Definition of the basic formalism–Reasoning algorithms– Language extensions - Complexity of Reasoning– Introduction- OR- branching: finding a model - AND- branching: finding a clash – Combining sources of complexity- Reasoning in the presence of axioms –Undecidability - Reasoning about individuals in ABoxes-A list of complexity results for ubsumption and satisfiability– Relationships with other Formalisms.
Unit V Hrs 18
AI knowledge representation formalisms - Logical formalisms - Database models Expressive Description Logics- Introduction - Correspondence between Description Logics and Propositional Dynamic Logics - Functional restrictions - Qualified number restrictions- Objects- Fixpoint constructs - Relations of arbitrary arity - Finite model reasoning - Undecidability results - Extensions to Description Logics – Introduction- Language extensions- Non-standard inference problems.