# Is first-order logic the same as predicate logic?

## Is first-order logic the same as predicate logic?

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

What is a predicate in first-order logic?

In logic, a predicate is a symbol which represents a property or a relation. For instance, the first order formula , the symbol is a predicate which applies to the individual constant .

### Which of these in first-order logic is used to make assertion about the objects?

The Universal Quantifier. What makes first-order logic powerful is that it allows us to make general assertions using quantifiers. The universal quantifier ∀ followed by a variable x is meant to represent the phrase “for every x.” In other words, it asserts that every value of x has the property that follows it.

What are the elements associated with a first order predicate calculus?

A first order (formal) language consists of constants, variables, logical symbols, and auxiliary symbols. It is said that a first order language L is given when all constants are given. In every argument, it is assumed that a language L is fixed and hence the phrase “of L” is omitted.

#### Is predicate logic complete?

Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement consisting of a single propositional variable A is not a theorem, and neither is its negation).

What is first order logic examples?

Definition A first-order predicate logic sentence G over S is a tautology if F |= G holds for every S-structure F. Examples of tautologies (a) ∀x.P(x) → ∃x.P(x); (b) ∀x.P(x) → P(c); (c) P(c) → ∃x.P(x); (d) ∀x(P(x) ↔ ¬¬P(x)); (e) ∀x(¬(P1(x) ∧ P2(x)) ↔ (¬P1(x) ∨ ¬P2(x))).

## What are the limitations of predicate logic?

One key limitation is that it applies only to atomic propositions. There is no way to talk about properties that apply to categories of objects, or about relationships between those properties. That’s what predicate logic is for.

What is the difference between propositional and predicate logic?

Propositional logic is the logic that deals with a collection of declarative statements which have a truth value, true or false. Predicate logic is an expression consisting of variables with a specified domain. It consists of objects, relations and functions between the objects.

### What is an example of a predicate?

A predicate is the part of a sentence, or a clause, that tells what the subject is doing or what the subject is. Let’s take the same sentence from before: “The cat is sleeping in the sun.” The clause sleeping in the sun is the predicate; it’s dictating what the cat is doing. Cute!

What is a valid formula of first-order logic?

A first-order formula F over signature σ is satisfiable if A |= F for some σ-structure A. If F is not satisfiable it is called unsatisfiable. F is called valid if A |= F for every σ-structure A. Given a set of formulas S we write S |= F to mean that every σ-structure A that satisfies S also satisfies F.