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

Difference between aggregation and association, Difference between aggregat...

Difference between aggregation and association Aggregation is a particular form of association, not an independent concept. Aggregation acts semantic connotations. If two objec

Define linear probing with respect to hashing technique, Define Linear Pro...

Define Linear Probing Linear Probing:  The easiest way to resolve a collision is to begin with the hash address and do a sequential search by the table for an empty location.

Convert logic circuit to minimised, The logic circuit shown in the given fi...

The logic circuit shown in the given figure can be minimised to Ans. The minimised figure of logic diagram is D, the output of the logic circuit is as Y=(X+Y')'+(X'+(X+

Show types under which networks will be divided, What are the two broad typ...

What are the two broad types under which Networks will be divided? Ans: All computer networks fit in one of the two dimensions specifically: a)  Transmission Technology, thi

Computer architecture, Explain division and its restoring and non-restoring...

Explain division and its restoring and non-restoring techniques?

Existential construction - artificial intelligence, The English existential...

The English existential construction involves so-called there-sentences such as these: (1)  There is a dog in the yard (2)  There were no children at the party (3)  There

What are the advantages of carrying out simulations, What are the Advantage...

What are the Advantages of carrying out simulations -  saves cost (instead of doing the real thing) -  Safer (scenarios tried out on the simulation first before used in real

Draw layout cells in a table, Now add layout cells into which you will add ...

Now add layout cells into which you will add text about travel locations. 1.  In Objects panel, click the Draw Layout Cell icon and move the pointer to layout table you just dre

Visibility, hidden edge/surface removal

hidden edge/surface removal

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