Introduction to Computational Logic

Name: Introduction to Computational Logic
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Propositional Logic, Natural Rules for Deduction, Derived Rules for Deduction, and Predicate Logic

Created byDr.Deeba K

Last updated 9/2023

English

English [Auto],

What you'll learn

Understand the basics of Propositional logic
Acquire skills on natural detection rules to handle Propositional logic
Acquire skills on derived rules to handle Propositional logic
Understand the First order Logic

Course content

6 sections • 21 lectures • 4h 8m total length

Introduction2:15
Explore computational logic by translating natural language statements into proportional logic, deriving reasoning rules through natural deduction, and extending to predicate logic for processing.
Introduction to Propositional Logic18:19
Explore propositional logic by modeling declarative statements with atomic variables and constants, and combine them with negation, disjunction, and implies to form well-formed formulas with clear precedence.
Unique Parsing11:17
Explore unique parsing in propositional logic, detailing well-formed formulas, proof by induction, basic steps, and how to derive formulas using negation, conjunction, disjunction, and implication.
Determining Proper Propositions12:09
Apply a formal algorithm to determine whether a string constitutes a well-formed, valid proposition in propositional logic, using a defined alphabet, connectors, and parentheses.
Interpretation of Propositional Logic Statement14:01
Explore interpretation of a propositional logic statement by assigning truth values, using valuations and models, and applying semantic entailment to assess validity and satisfiability.
Assessment in Introduction to Propositional Logic

Natural Deduction rules12:54
Master natural deduction rules and translate statements into propositions to derive valid conclusions from premises. Apply implication introduction and elimination, negation, and double negation elimination to build deductive sequences.
Validating Sequent using Natural Deduction16:20
Explore validating sequents via natural deduction, applying introduction and elimination rules to derive conclusions from premises and assumptions. Learn about negation, implications, and proofs by contradiction using insertion and elimination.
Equivalence of two Propositional Logic Statements15:53
Demonstrates proving the equivalence of two propositional logic statements via natural deduction, using assumptions, implication elimination, and forward and reverse proofs to establish bidirectional validity.
Assessment in Natural Deduction

Derived Rules and Its proof11:13
Explore derived rules in natural deduction, including implication elimination, negation, and contradiction, and learn to derive conclusions with double negation and the law of excluded middle.
Examples of Derived rules7:22
Demonstrate derived rules through examples of negation, implication, and proof by contradiction, showing how to use elimination and double negation to prove or refute statements.
Sequent with Nil LHS10:15
Explore sequent with nil left-hand side, showing how assumptions and implications drive derivations in natural deduction, with insertion and elimination steps toward the conclusion.
Assessment in Derived Rules

Introduction to Predicate Logic8:41
Explore predicate logic, including universal and existential quantifiers, predicates with unary and binary arguments, and composing logic statements with variables, predicates, and function terms.
Term in Predicate Logic8:31
Explore predicate logic terms and normal forms, distinguishing bound and free variables, quantifier scope and binding priority, and how substitutions affect formulas.
Model in Predicate Logic6:46
Explore how a predicate logic model interprets variables, predicates, and functions through substitutions. Learn to use universal and existential quantifiers and state transition diagrams to assess statement validity.
Parse Tree, Free and Bounded variables16:33
This lecture explains constructing a parse tree for predicate logic, outlining binary and unary operators, and identifying free and bounded variables within quantifier scopes.
Assessment in Predicate Logic

Natural Deduction rules in FOL6:08
Explore natural deduction rules in first-order logic, combining propositional and predicate logic. Learn how universal and existential quantifiers, equality insertion and elimination, and introduction and elimination rules apply.
Deduction for Universal Quantifiers15:03
Explore applying universal and existential quantifier rules in natural deduction for predicate logic, including for all introduction, elimination, and exists insertion and elimination.
Rule for Equivalence11:49
Explore quantifier equivalence in natural deduction by proving it in both directions, using existential and universal quantifiers, introduction and elimination rules.
Deriving Provable equivalence using Natural Deduction3:58
Explore deriving provable equivalence with natural deduction by applying equality insertion and elimination, using substitution to transform premises like T1 = T2 and T2 = T3 into T1 = T3.

Kripke's Model20:11
Explore Kripke's model as an extension of propositional logic, introducing square and diamond modalities, semantic entailment, and models with worlds, relations, and labeling functions.
Computational Tree Logic19:07
Explains computational tree logic as branching time logic on a non-deterministic infinite tree, using A/E modalities, next/global/until operators, and parse trees to assess formula validity.

Requirements

No prerequisites are there for this course. Students can listen to the lectures to understand computational logic concepts from base.

Description

The aim of logic in computer science is to develop languages to model the situations we encounter as computer science professionals, in such a way that we can reason about them formally. Reasoning about situations means constructing arguments about them; we want to do this formally, so that the arguments are valid and can be defended rigorously, or executed on a machine.

In order to make arguments rigorous, we need to develop a language in which we can express sentences in such a way that brings out their logical structure. The language we begin with is the language of propositional logic. It is based on propositions, or declarative sentences which one can, in principle, argueas being true or false.

The outline of this course is given as,

Introduction to Propositional Logic, Parse tree, valuation of Propositional Logic statements, Model in propositional logic

How do we go about constructing a calculus for reasoning about propositions given a certain arrangement of premises. - Natural Rules for Deduction, Examples of Natural Deduction Rules

Derived Rules for Deduction, Proof by contradiction, Modus Tollens,Law of Excluded middle portion and Double negation elimination

Introduction to Predicate Logic, Natural language statements to Predicate logic statements

Parse tree, substitution and Model in First order logic

Who this course is for:

Computer science students
Students who wants to learn computational logic
Anybody who wants to pursue a career in Computer Science Engineering

Introduction to Computational Logic

What you'll learn

Explore related topics

Course content

Introduction to propositional Logic5 lectures • 58min

Natural Deduction of Propositional Logic3 lectures • 45min

Derived rules for Propositional Logic3 lectures • 29min

Introduction to Predicate Logic4 lectures • 41min

Natural Deduction in Predicate Logic4 lectures • 37min

Introduction to Kripke's Model and CTL2 lectures • 39min

Requirements

Description

Who this course is for: