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

How and what data is gathered- simulation, How and what data is gathered- S...

How and what data is gathered- Simulation To make this as realistic as possible, data is required to be gathered over a long period of time. This can be done by sensors near/i

Corrosion, Explain the mechanidm of the rusting of iron on the basis of ele...

Explain the mechanidm of the rusting of iron on the basis of electrochemical corrosion?

Realize the basic gates with any one universal gate, What is a universal ga...

What is a universal gate? Give examples. Realize the basic gates with any one universal gate. Ans: Universal Gates:   NAND and NOR are termed as Universal gates. The OR, AN

What qualifications needs to be an security professionals, Qualifications o...

Qualifications of security professionals For the security professionals, it is essential that they have adequate freedom to check the security measures and enforce them and

Main problems with evaluation functions, Main problems with evaluation func...

Main problems with evaluation functions: Superlatively, evaluation functions should be quick calculates. Wherever is chance they take a long time to estimate, so after then le

Introduction to e-commerce, Have you heard about e-commerce? What place is ...

Have you heard about e-commerce? What place is e-commerce located at? What are e-commerce objectives? When did e-commerce starts? How e-commerce works? Who takes advantages of e-co

Recursive procedures are implemented, Recursive procedures are implemented ...

Recursive procedures are implemented by using Recursive procedures are executed by using stacks due to stacks are LIFO data structure and we require this feature to store retur

Why should you use bugzilla?, Bugzilla can dramatically enhance the product...

Bugzilla can dramatically enhance the productivity and accountability of individual employees by giving a documented workflow and positive feedback for good performance.

Self-perception, Mr. X seems to view himself in positive terms (MMPI-2: Ho=...

Mr. X seems to view himself in positive terms (MMPI-2: Ho=38) as a well-functioning person who is capable of dealing with his life and personal challenges (MMPI-2: LSE=41, TRT=39),

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