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

Subtract, Write the Add/subtract rule for floating point numbers. Ans:...

Write the Add/subtract rule for floating point numbers. Ans: a. Select the number with the smaller exponent and shift its mantissa right a number of steps equal to the differe

forensics capability relevant to a honeynet server, A local government org...

A local government organisation needs to deploy a honey net. To this end you are to deploy a honeynet based on the supplied network diagram (separate download) that should give sop

Explain the matlab mathematical function library?, This is a huge collectio...

This is a huge collection of computational algorithms ranging from elementary functions like sum, sine, cosine, and difficult arithmetic, to more sophisticated functions like matri

Implementation of a simple arithmetic, Q. Implementation of a Simple Arithm...

Q. Implementation of a Simple Arithmetic? So, by now we have concerned how logic and arithmetic micro-operations can be applied individually. If we combine these 2 circuits alo

Illustrate the basic structure of the von neumann machine, Illustrate the b...

Illustrate the basic structure of the von Neumann machine The following figure shows basic structure of the von Neumann machine. A von Neumann machine has only a single path be

What is a screen group, What is a screen group? How it is useful? Scre...

What is a screen group? How it is useful? Screen group is a field in the Screen Attributes of a screen.  Here we can explain a string of up to four characters which is availa

Biological motivation - two layer artificial neural networks, Biological Mo...

Biological Motivation : However remember there that in discussion first lecture is about how people have answered the question like: "How are we going to get an agent to proce

Define the internal users of system, Q. Define the Internal Users of system...

Q. Define the Internal Users of system? Internal Users are employees of business for that an information system is built. Illustration are clerical and service staff, technic

Classification of interrupts - computer architecture, Classification of int...

Classification of interrupts:   1. a) asynchronous   external components or hardware malfunction 1.b)synchronous   function of program state (for example over

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