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

Explain why the ROM is a volatile memory, Is the ROM a volatile memory? Exp...

Is the ROM a volatile memory? Explain Ans. No, ROM is a Non-Volatile memory. Programming of ROM includes making of the needed  interconnections at  the time of fabrication and

Networking, how to connect a home network

how to connect a home network

What do you mean by digital computer, COMPUTER ORGANIZATION & ARCHITECTURE ...

COMPUTER ORGANIZATION & ARCHITECTURE 1. What do you mean by digital computer? Explain the block diagram of a digital computer. 2. What do you mean by Difference Engine? Expl

Ellipse follows the perimeter of the window, A) Execute a program where an ...

A) Execute a program where an ellipse follows the perimeter of the window. B)  Execute a program that can draw graphs, possibly following your plan from last week. Have it graph

Control-centered virtual manufacturing, Control-Centered Virtual Manufactur...

Control-Centered Virtual Manufacturing This is the addition of simulations to control actual processes and models, permitting for seamless simulation for optimization throughou

How can i delete a file, The Standard C Library function is removing. (This...

The Standard C Library function is removing. (This is thus one of the few questions in this section for which the answer is not ''It's system-dependent.'') On older, pre-ANSI Unix

Program for encoding ASCII alpha numeric, Q. Program for encoding ASCII Alp...

Q. Program for encoding ASCII Alpha numeric? ; A program for encoding ASCII Alpha numeric. ; ALGORITHM:             ; create the code table             ; read an input

Explain clearly the kuleshov experiment, Question: (a) Write a proposal...

Question: (a) Write a proposal for a 10-11 minutes movie of your choice with the expected content. (b) Explain clearly the "Kuleshov Experiment" (c) Give the checklist be

What is low-level formatting, What is low-level formatting?  Before a d...

What is low-level formatting?  Before a disk can store data, it must be divided into sectors that the disk controller can read and write. This process is known as low-level for

Process of world wide web, Q. Process of World Wide Web? When you type ...

Q. Process of World Wide Web? When you type a URL in a web browser, this is what happens: 1. If URL contains a domain name, browser first connects to a domain name server an

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