Propositional logic- formal language Propositional Logic (PL) is a formal language, which has syntax, a set of symbols, and semantics. It is not a natural language such as English. All…

The logic of soundness and completeness The logic of soundness and completeness is to check whether a formula φ is valid or not. To prove a given formula φ, there are…

Conjunctive normal form A literal L is either an atom p or the negation of an atom ¬p. If a formula is a conjunction of clauses, where each clause D…

Horn clauses and satisfiability Horn formulas are conjunctions of Horn clauses. Horn clauses are an implication whose assumption (left side of the arrow) A is a conjunction of the proposition…

Predicate Logic A predicate is a statement that contains variables (predicate variables) and that may be true or false depending on the values of these predicate variables. Predicates are the…

Term and formula in Predicate logic A Formal Language Predicate Logic provides a way to formalize natural language so that ambiguity is removed. A predicate logic formula involved two sorts of…

Prolog-Logical Paradigm Prolog, Programming in logic, is a declarative programming language that is based on the ideas of logic programming. Prolog was an idea to make the logic look like…

Declarative sentence Declarative Sentence (Statement) makes a statement, states a fact or an argument and ends with a full stop/period. It declares something, as it is named appropriately. Declarative sentences…

Propositional logic-introduction Propositional logic or 0th order is the branch of logic that studies ways of joining as well as modifying entire propositions, statements or sentences to form a more…

Natural deduction Natural deduction System for a structured deduction from a set of assumptions, based on rules, specific to the logical connectives. The way of proving that an argument is…