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

Strategy used for the project design, This project is divided to two parts ...

This project is divided to two parts (hardware and software) each with is subtask and consideration was given in all areas in order to meet the target specification. Solutions are

Determine the equivalent in octal of decimal number, Convert decimal 153 to...

Convert decimal 153 to octal. Equivalent in octal will be ? Ans. (153) 10 = (231) 8

Design goals of computer system, Design goals: The correct form of a c...

Design goals: The correct form of a computer system depends on the constraints and aim for which it was optimized. Computer architectures frequently trade off   cost, standard

ERP, Benefits of implementing ERP

Benefits of implementing ERP

Show the major benefits of microprocessor, Q. Show the Major benefits of mi...

Q. Show the Major benefits of microprocessor? Microprocessor is a complete CPU on a single chip. The major benefits of microprocessor are:  Powerful butCompact; can

Give difference between compiler and interpreter, Give difference between c...

Give difference between compiler and interpreter. Compiler: It is a translator for machine independent HLL as FORTRAN and COBOL etc. Interpreter: It analysis the source

Explain the term - rational rose and visio 2000 enterprise, Explain the ter...

Explain the term - Rational Rose and Visio 2000 Enterprise Rational Rose: IBM Rational RequisitePro is a powerful and easy-to-use tool for use case management and requirement

Determine the uses of smart cards, Determine the uses of Smart cards  ...

Determine the uses of Smart cards  These comprise embedded microchips and receive power from the card readers; Microchip is made up of RAM, ROM and 16-bit processor and the st

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