Variables and quantifiers for first-order models , Computer Engineering

Assignment Help:

Variables and Quantifiers for First-order models -artificial intelligence:

So what do sentences containing variables mean? In other words, how does first order model select whether such a sentence is false ortrue? The first step is to ensure that the sentence does not contain any unrestricted variables, variables which are not bound by (associated with) a quantifier. Firmly speaking, a first-order expression is not a sentence unless all the variables are bound. However, we typically assume  that  if  a  variable  is  not  explicitly  bound  then  actually  it  is  implicitly commonly quantified.

Next we look for the outermost quantifier in our sentence. If it is   X then we consider the truth of the sentence for each value X could take. When the outermost quantifier is   X we have to search only a single possible value of X. To make it more formal we may use a concept of substitution. Here {X\t} is a substitution that replaces all occurrences of variable X with a term representing an object t:

  • X. A is true if and only if A.{X\t} for all t in Δ
  • X. A is true if and only if A.{X\t} for at least one t in Δ

Repeating this for all the quantifiers we get a set of ground formulae which we have to check to see if the original sentence is true or false. Unluckily, we haven't specificed that our domain Δ is finite for an example, it may contain the natural numbers - so there may be a infinite number of sentences to check for a given model! There may be also be an infinite number of models .So even though we have a right definition of model, and so a proper semantics for first-order logic, so we cannot  rely  on  having  a  finite  number  of  models  as  we  did  when  drawing propositional truth tables.


Related Discussions:- Variables and quantifiers for first-order models

Explain about truth table and logic diagram, Q. Explain about truth table a...

Q. Explain about truth table and logic diagram? A Boolean function can be realized in a logic circuit employing the basic gates: - AND, OR & NOT. Concern here for illustration

Register transfer micro-operations, Register Transfer Micro-operations ...

Register Transfer Micro-operations These micro-operations as the name proposes transfer information from one register to another. The information doesn't change during these mi

What is meant by hide area, What is meant by hide area? The hide comman...

What is meant by hide area? The hide command temporarily kept the contents of the field at the present line in a system-controlled memory called as the HIDE AREA.  At an intera

State the types of common toes deformities a, Common toes deformities are: ...

Common toes deformities are: 1. Hallux valgus: Deviation of great toe towards the second toe resulting in prominence of first metatarsal head.  Later on there is formation of

What is an html tag, An HTML tag is a syntactical construct in the HTML lan...

An HTML tag is a syntactical construct in the HTML language that abbreviates particular instructions to be implemented when the HTML script is loaded into a Web browser. It is like

What is the main function of a browser, The main function of a browser is t...

The main function of a browser is to? The important function is to interpret HTML of a browser.

Explain call by value and call by reference, Call by value and Call by refe...

Call by value and Call by reference Call by value means sending the values of the arguments- The value of each of the original arguments in the calling function is copied in

Search mechanisms in prolog - artificial intelligence, Search mechanisms in...

Search mechanisms in Prolog We can utilize this simple Prolog program to describe how Prolog searches: president(X) :- first_name(X, georgedubya), second_name(X, bush). p

++ c, how to find the integral of a function represented by collection of e...

how to find the integral of a function represented by collection of experimental data

Which device converts BCD to seven segment, A device which converts BCD to ...

A device which converts BCD to Seven Segment is called ? Ans. DECODER is a device that converts BCD to Seven Segment. This coverts binary words in alphanumeric characters.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd