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

Connection machine fortran, Q. Connection Machine FORTRAN? Connection M...

Q. Connection Machine FORTRAN? Connection Machine Fortran was a subsequent SIMD language developed by Thinking Machines Corporation. Connection Machine Fortran incorporated all

Describe the role of software developers, Describe the role of Software dev...

Describe the role of Software developers Software developers have wide experience of tackling such issues. Students who develop software project spending days and nights strug

Ready and standard mode for point-to-point message passing, Q. Ready and St...

Q. Ready and Standard mode for point-to-point message passing? Ready mode: Transmitting can be started only if matching receive has already been initiated.  Standard mode: M

What is a cgi bin directory, A CGI bin directory is a special directory on ...

A CGI bin directory is a special directory on the server where CGI scripts are allowed to be implemented. Most servers are configured to only permit CGI scripts to be implemented f

Combinational logic, At a particular moment in time the output of a COMBINA...

At a particular moment in time the output of a COMBINATIONAL logic circuit depends uponthe inputs to the circuit at the same instant.(Unlike sequential logic circuits where the out

What are advantages and drawbacks of flip-flop, What are advantages and dra...

What are advantages and drawbacks of flip-flop? Usually area of a Flip-flop for features in more than a latch. Power consumption is normally higher, because of the area and

Add the equation by using 2's compliment, Add 20 and (-15) using 2's comple...

Add 20 and (-15) using 2's complement ? Ans. Addition of 20 and (-15) by using 2's complement as (20) 10 = 1 0 1 0 0                                                  (16

Describe how a mobile terminating call, Problem: (a) Describe how a Mob...

Problem: (a) Describe how a Mobile Terminating call, from a PSTN phone, is processed in a GSM network. Illustrate your answer with a diagram. (b) What is a GPRS Support node

How optimization is achieved in dns, How optimization is achieved in DNS? ...

How optimization is achieved in DNS? Two primary optimizations used in DNS and they are: replication and caching. All root servers is replicated; various copies of the server

Contain your variable names and definitions, Give your analysis for the fol...

Give your analysis for the following problem statement: You require to write a program that calculates the area and perimeter of a rectangle whose dimensions (Length &width) are gi

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