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

Command line argument value, Make a console application to show different m...

Make a console application to show different messages depending on the command line argument value. Use Select-case statements.(same to switch block)

What is skew, What is skew? Clock Skew: In circuit design, clock ske...

What is skew? Clock Skew: In circuit design, clock skew is a phenomenon within synchronous circuits wherein the clock signal (sent through the clock circuit) arrives at dive

What is file allocation table, Q. What is File allocation table? FAT ma...

Q. What is File allocation table? FAT maps the usage of data space of disk. It comprises information about space used by every individual file and unused disk space as well as

Define mercantile process model from perspect of merchant, Define Mercantil...

Define Mercantile Process Model from the Merchant’s perspective along with a suitable diagram. This model consists of three activities into the purchase consummation phase: Aut

Why gateways are used during mail transfer, Why Gateways are used during ma...

Why Gateways are used during mail transfer? Email using SMTP effort best while both the sender and the receiver are on the internet and can hold TCP connections in between send

QUELING SYTEM , SHOW THAT AVERAGE NUMBER OF UNIT IN A (M/M/1) QUELING SYTEM...

SHOW THAT AVERAGE NUMBER OF UNIT IN A (M/M/1) QUELING SYTEM IS EQUAL TO P/(1-p). NOTE:P=ROW

Linux, Explain about unix file system architecture

Explain about unix file system architecture

Control signal, justify whether the control signal passes through same bus ...

justify whether the control signal passes through same bus as data ,address and instruction or not?

Write a .net web service program, Question: (a) Give three typical use...

Question: (a) Give three typical uses of Web Services. (b) Describe the term WebService Behavior and list its advantages. (c) Explain how Proxy classes are used to acc

What is the meaining of action implementing instruction, Action implementin...

Action implementing instruction's meaning are a actually carried out by ? Ans. By instruction execution, the meaning of action implementing instruction is actually carried out.

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