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

Failures, FAILURES Since reliability engineering is focused on the surv...

FAILURES Since reliability engineering is focused on the survivability or absence of failures, it is more concerned about failures,  understanding  their causes and defining re

Define pipeline speedup, Define pipeline speedup. S(m)=T(l)/T(m) Whe...

Define pipeline speedup. S(m)=T(l)/T(m) Where T(m) is the execution time for some target workload on an m-stage pipeline. T(l) is the execution time for some workload an

What is a pre-processor, What is a pre-processor? A pre-processor is a ...

What is a pre-processor? A pre-processor is a program that procedure the source code before it passes by the compiler. It handles under the control of pre-processor directive.

Describe critical directive in fortan, Q. Describe Critical Directive in FO...

Q. Describe Critical Directive in FORTAN? The critical directive permits one thread executes associated structured block. When one or more threads attain critical directive the

Explain the random scan and raster scan displays, Define Random scan/Raste...

Define Random scan/Raster scan displays?  Random scan is a method in which the display is made by the electronic beam which is directed only to the points or part of the screen

Computer graphics, explain area sub division method algorithm

explain area sub division method algorithm

Explain criteria for selection of suitable intermediate code, Pass I of the...

Pass I of the assembler must also generate the intermediate code for the processed statements. Justify your answer. Criteria for selection of a suitable intermediate code form

Classified the vlsi technology, The VLSI technology is still developing. Mo...

The VLSI technology is still developing. More and more powerful microprocessors and more storage space now are being put in single chip. One question that we have still not conside

Write an html program segment that contains hypertext links, Write an HTML ...

Write an HTML program segment that contains hypertext links from one document to another . HTML permits any item to be placed as a hypertext reference. Therefore a single word

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