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

Determine what is the frame rate and frame duration, (i)  A multiplexer com...

(i)  A multiplexer combines four 100-Kbps channels using a time slot of 4 bits. Each Frame has the size of 16 bits. a)  Show the output with the four inputs as shown in the figu

Conversion of bcd number to binary using a procedure, Q. Conversion of BCD ...

Q. Conversion of BCD number to binary using a procedure? Conversion of BCD number to binary using a procedure. Algorithm for conversion procedure: Take a packed BCD digit

List criteria of data structures used in language processing, List the crit...

List the criteria on the basis of which data structures used in language processing can be classified. In language processing the data structures utilization can be classified

Describe the fundamental characteristics of antennas, Question 1: (a) ...

Question 1: (a) Describe the two fundamental characteristics of antennas explaining in detail how it affects the security of wireless networks. (b) What is a wireless cli

Show the layout of dvorak-dealey keyboard, Q. Show the layout of Dvorak-Dea...

Q. Show the layout of Dvorak-Dealey keyboard? This was one keyboard layout designed to be a challenger to QWERTY layout. This was designed by August Dvorak and William Dealey a

Explain about server synchronization, Q. Explain about Server synchronizati...

Q. Explain about Server synchronization? Server synchronization: It updates atom by server process of requesting process. In this method an atom acts as a unique update server.

Explain classless inter-domain routing, Explain Classless Inter-Domain Rout...

Explain Classless Inter-Domain Routing. It is a new addressing scheme for the internet that permits for more efficient allocation of IP addresses than old class A, B and C addr

Programs, A palindrome is a string that reads the same from both the ends. ...

A palindrome is a string that reads the same from both the ends. Given a string S convert it to a palindrome by doing character replacement. Your task is to convert S to palindrome

Explain about indexed addressing scheme, In this technique, operand field o...

In this technique, operand field of instruction includes an address and an index register thatcomprises an offset. This addressing scheme is normally used to address the consecutiv

Determine the handles data rate of broad band isdn, Broad Band ISDN handles...

Broad Band ISDN handles data rate of about (A) 64 kbps                                      (B) 100 mbps (C) 5.4 mbps                                    (D) 2.048 mbps

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