Contents

## How do you translate a sentence into first order logic?

*Bill takes analysis if an namely if you will not take geometry up with bill takes analysis no geometry. But not both at the same time those two vasilich. Night. So she throws in a bill Kabila crow.*

## How do you translate sentences into predicate logic?

*And we could also establish that hx could be x is happy now it's important that you put the variable there that tells us basically what we're substituting.*

## How do you read first order logic?

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,…. |
---|---|

Variables | x, y, z, a, b,…. |

Predicates | Brother, Father, >,…. |

Function | sqrt, LeftLegOf, …. |

Connectives | ∧, ∨, ¬, ⇒, ⇔ |

## How do I translate English to logic?

*So if you have the sentence dogs aren't people you'd symbolize this as not d because all of your propositions should be in the affirmative. And then you use the negation to represent that not.*

## 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.

## Is FOL 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 first order rules?

**Free and bound variables of a formula need not be disjoint sets**: in the formula P(x) → ∀x Q(x), the first occurrence of x, as argument of P, is free while the second one, as argument of Q, is bound. A formula in first-order logic with no free variable occurrences is called a first-order sentence.

## What is one advantage or disadvantage of FOL?

It is also called first order logic (FOL). The obvious advantage is that **we can say a lot more**. One disadvantage is that while theorem proving is still sound, (that is, we can always prove true theorems), it is now undecidable (the theorem prover may never halt on untrue statements).

## What is first order formula?

A first-order differential equation is defined by an equation: **dy/dx =f (x,y)** of two variables x and y with its function f(x,y) defined on a region in the xy-plane. It has only the first derivative dy/dx so that the equation is of the first order and no higher-order derivatives exist.

## What are alphabets used for first-order logic?

First order logic consists of an alphabet, a first order language, a set of axioms and a set of inference rules. The alphabet consists of seven classes of symbols: Variables – A sequence of alphanumeric characters that refer to objects in the domain. e.g. **u, v, w, x, y, z, foo**.

## What is knowledge engineering in FOL?

**The process of constructing a knowledge-base in first-order logic** is called as knowledge- engineering. In knowledge-engineering, someone who investigates a particular domain, learns important concept of that domain, and generates a formal representation of the objects, is known as knowledge engineer.

## Why is FOL undecidable?

First-order logic is complete because all entailed statements are provable, but is undecidable because **there is no algorithm for deciding whether a given sentence is or is not logically entailed**.

## 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.

## Is first-order logic consistent?

By PROPOSITION 3.5 we know that **a set of first-order formulae T is consistent if and only if it has a model**, i.e., there is a model M such that M N T. So, in order to prove for example that the axioms of Set Theory are consistent we only have to find a single model in which all these axioms hold.

## What is a valid formula of first-order logic Any examples?

Any uniform substitution of first-order formulae for the propositional variables in a propositional formula A produces a first-order formula, called a first-order instance of A. Example: take the propositional formula **A = (p ∧ ¬q) → (q ∨ p)**. ((5 < x) ∧ ¬∃y(x = y2)) → (∃y(x = y2) ∨ (5 < x)). and |= P(x) ∨ ¬P(x).

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

## 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.

## What is a formula in FOL?

FOL formula literal, **application of logical connectives**. **(¬, ∨ , ∧ , → , ↔ ) to formulae,** **or application of a quantifier to a formula**. 2- 4. Page 2.

## What is an atomic formula in FOL?

Atomic formula in first-order logic

An atomic formula or atom is simply **a predicate applied to a tuple of terms**; that is, an atomic formula is a formula of the form P (t_{1} ,…, t_{n}) for P a predicate, and the t_{n} terms. All other well-formed formulae are obtained by composing atoms with logical connectives and quantifiers.