MullOverThings

Useful tips for everyday

# Is first-order logic decidable?

## Is first-order logic decidable?

First-order logic is not decidable in general; in particular, the set of logical validities in any signature that includes equality and at least one other predicate with two or more arguments is not decidable. Logical systems extending first-order logic, such as second-order logic and type theory, are also undecidable.

## Is predicate logic and first-order logic same?

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 are the advantages of description logics over first order logics?

Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic.

## Why is first order predicate logic more expressive than propositional logic?

First-order logic is another way of knowledge representation in artificial intelligence. It is an extension to propositional logic. FOL is sufficiently expressive to represent the natural language statements in a concise way. First-order logic is also known as Predicate logic or First-order predicate logic.

## When we say a problem is decidable?

A problem is said to be Decidable if we can always construct a corresponding algorithm that can answer the problem correctly. We can intuitively understand Decidable problems by considering a simple example. Suppose we are asked to compute all the prime numbers in the range of 1000 to 2000.

## Is propositional 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).

## Is propositional logic better than FOPL?

Key differences between PL and FOL Propositional Logic converts a complete sentence into a symbol and makes it logical whereas in First-Order Logic relation of a particular sentence will be made that involves relations, constants, functions, and constants.

## What is predicate logic example?

For example, suppose M is the predicate representing “man is mortal” and let x be a variable. Then M(x) is an atomic formula meaning “x is mortal.” So, as we know, a predicate is an expression of one or more variables defined on some domain, and an atom is the most straightforward well-formed formula in logic.

## 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 is logic in knowledge representation?

Description logic denotes a family of knowledge representation formalisms that model the application domain by defining the relevant concepts of the domain and then using these concepts to specify properties of objects and individuals occurring in the domain (Baader and Nutt 2003).