# What exactly is a first-order logic?

First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as “Socrates is a man”, one can have expressions in the form “there exists x such that x is Socrates and x is a man”, where “there exists” is a quantifier, …

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## What is first-order logic?

First-order logic is symbolized reasoning in which each sentence, or statement, is broken down into a subject and a predicate. The predicate modifies or defines the properties of the subject. In first-order logic, a predicate can only refer to a single subject.

## What is first-order logic with example?

The basic syntactic elements of first-order logic are symbols. We write statements in short-hand notation in FOL.

Basic Elements of First-order logic:

Constant 1, 2, A, John, Mumbai, cat,….
Function sqrt, LeftLegOf, ….
Connectives ∧, ∨, ¬, ⇒, ⇔
Equality ==
Quantifier ∀, ∃

## What is first-order logic in AI?

FOL is a mode of representation in Artificial Intelligence. It is an extension of PL. FOL represents natural language statements in a concise way. FOL is also called predicate logic. It is a powerful language used to develop information about an object and express the relationship between objects.

## What is first-order and second order logic?

First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic has these variables as well as additional variables that range over sets of individuals.

## Why do we need first-order logic?

To generalise, first-order logic allows us to get at the internal structure of certain propositions in a way that is not possible with mere propositional logic. The possession or non-possession of important logical properties turns on the precise nature of these internal structures.

## What is the difference between propositional logic and first-order logic?

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.

## How do you write first-order logic?

Let's take one statement. You know X is in diesel. Okay. X is an integer. Now subject is nothing but in every statement. We not talk about something that is subject. Okay so here we are talking about

## Is first-order logic complete?

Perhaps most significantly, first-order logic is complete, and can be fully formalized (in the sense that a sentence is derivable from the axioms just in case it holds in all models). First-order logic moreover satisfies both compactness and the downward Löwenheim-Skolem property; so it has a tractable model theory.

## What is the role of logic in artificial intelligence?

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.

## Is first-order logic incomplete?

First order arithmetic is incomplete. Except that it’s also complete. Second order arithmetic is more expressive – except when it’s not – and is also incomplete and also complete, except when it means something different. Oh, and full second order-logic might not really be a logic at all.

## Why is second-order logic incomplete?

Theorem: 2nd order logic is incomplete: 1) The set T of theorems of 2nd order logic is effectively enumerable. 2) The set V of valid sentences of 2nd order logic is not effectively enumerable. 3) Thus, by Lemma One, V is not a subset of T.

## What do you mean by propositional logic?

Propositional logic, also known as sentential logic, is that branch of logic that studies ways of combining or altering statements or propositions to form more complicated statements or propositions. Joining two simpler propositions with the word “and” is one common way of combining statements.

## 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).