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

Find out the 2's complement of 1101110, The 2's complement of the number 11...

The 2's complement of the number 1101110 is ? Ans. 1's complement of 1101110 is = 0010001 ans hence 2's complement of 1101110 is = 0010001 + 1 = 0010010.

Computer, How does computer started?

How does computer started?

Explain cpu based exchange, Explain CPU based exchange. CPU Based Exch...

Explain CPU based exchange. CPU Based Exchange: All the control equipment is replaced with a single processor that must be quite powerful, in centralized control. This should

Translation look aside buffer - computer architecture, Translation Look asi...

Translation Look aside Buffer :    A TLB is a cache that holds only page table mapping If there is no matching entry in the TLB for a page ,the page table have to

Logical database reads the data from the database, Is it true that the Logi...

Is it true that the Logical Database reads the data from the database tables using Select Statements. Yes. We are coding that in Database part of LDB.

Where telephone traffic is measured, Telephone Traffic is measured in ...

Telephone Traffic is measured in (A)  Seconds.  (B)  Hours. (C)  Erlang       (D)  Pulses per minute. Ans: Telephone Traffic is measured in Erlang.

How does tcp take of wrapping over of sequence numbers, How does TCP take o...

How does TCP take of wrapping over of sequence numbers? To handle out of instruct deliveries, transport protocols utilize sequencing. The sending side attaches a sequence numbe

Raid and data stripping, Explained RAID? Ans: High performance devices ...

Explained RAID? Ans: High performance devices tend to be costly. So we can gain very high performance at a reasonable cost using a number of low-cost devices operating in paral

Briefly explain array processing in detail, Array Processing We have se...

Array Processing We have seen that for executing vector operations the pipelining conception has been used. There is other method for vector operations. If we have array of n p

What is flag, Flag is a flip-flop used to kept the information about the st...

Flag is a flip-flop used to kept the information about the status of a processor and the status of the instruction implemented most recently A software or hardware mark that si

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