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

What is internal path length, Internal Path length It is described as t...

Internal Path length It is described as the number of node traversed while moving by one particular node to any other node in the tree.

Convergence mean with respect to e-commerce, What does the term convergence...

What does the term convergence mean with respect to E-commerce? Convergence with respect to e-commerce   The ability to leverage and integrate the several data sources and

Define protocol, Define Protocol. It is a set of rules that are followe...

Define Protocol. It is a set of rules that are followed by interconnecting computers and terminals to make sure the orderly transfer of information

Define polling, Define Polling. A Polling process is used to recognize...

Define Polling. A Polling process is used to recognize the highest priority source by software means. In this process there is one common branch address for all interrupts.

What is memory mapped i/o, What is memory mapped I/O? When the I/O devi...

What is memory mapped I/O? When the I/O devices share the similar address space, the arrangement is known as memory mapped I/O.

Determine the process of action-object matrix, Determine the Process of act...

Determine the Process of action-object matrix Check for multiple models  Recognize objects Design user object model diagram Define user object actions De

With what symbolic names can be associated, Symbolic names can be associate...

Symbolic names can be associated with? Ans. With data or instruction symbolic names associated.

Illustrate 16-bit isa, Illustrate 16-bit ISA?  Compare it with 8-bit ISA bu...

Illustrate 16-bit ISA?  Compare it with 8-bit ISA bus.  The only difference between 8 and 16-bit ISA bus is that an extra connector is attached behind the 8-bit connector. 16-b

What are bags and sequences, What are bags and sequences? A bag is a co...

What are bags and sequences? A bag is a collection of elements with duplicates permitted.  A sequence is an ordered collection of elements with duplicates permitted.

Explain the working of a half subtractor, With the help of a truth table ex...

With the help of a truth table explain the working of a half subtractor. Draw the logic diagram using gates. Ans: Half Subtractor: For the subtraction of B (subtrahend) f

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