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 that datagram cannot be larger than mtu of a network, "A datagram c...

"A datagram cannot be larger than the MTU of a network over which it is sent." Is the statement true or false? Explain with the help of a suitable example. All hardware technol

What is race-around problem and how can you rectify this, What is Race-arou...

What is Race-around problem? How can you rectify this? The clock pulse which remains into the 1 state whereas both J and K are equal to 1 will reason the output to complement a

What is the main difference between asp and asp.net, What is the Main diffe...

What is the Main difference between ASP and ASP.NET ?   ASP contains scripts which are not compiled while in ASP.net the code is compiled.

Select-options and parameters statement , The fields specified by select-op...

The fields specified by select-options and parameters statement cannot be grouped together in the selection screen. No, the fields specified by select-options and parameters s

List the various file attributes, List the various file attributes. A f...

List the various file attributes. A file has certain other attributes, which differ from one operating system to another, but typically consist of these: Name, identifier, type

Physics, derive an expression for vandar wall equation of state?

derive an expression for vandar wall equation of state?

Explain r-2r ladder d/a converter, Explain R-2R ladder D/A converter. A...

Explain R-2R ladder D/A converter. Ans. R-2R ladder D/A converter: An R-2R ladder D/A converter is shown in Fig.(a). It uses resistors of only two values R and 2R. The inp

What are the types of assemblies, There are two types of assemblies:- 1...

There are two types of assemblies:- 1. Private Assemblies 2. Shared Assemblies

Internal organisation of memory chips, expplain in detail the internal orga...

expplain in detail the internal organisation of computer?

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