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 matrix addressing mode, What is Matrix Addressing Mode. Ans. M...

What is Matrix Addressing Mode. Ans. Matrix Addressing Mode: The arrangement which needs the fewest address lines is a square array of n rows and n columns for a whole memory

Describe about digital audio tape, Q. Describe about Digital Audio Tape? ...

Q. Describe about Digital Audio Tape? The most proper tape for backing up data from a disk today is Digital Audio Tape (DAT). It employs a 4mm tape covered in a cartridge. It e

Write a program that finds the minimum total number of shelv, Write a progr...

Write a program that finds the minimum total number of shelv, C/C++ Programming

What do you call an event and when do you call an assertion, What do you ca...

What do you call an event and when do you call an assertion? Assertion based Verification Tools, checks whether a statement holds a explained  property or not, while, Event bas

What is the kernel, What is the kernel?          A more common definiti...

What is the kernel?          A more common definition is that the OS is the one program running at all times on the computer ,usually  known as the kernel, with all else being

What is the significance timescale directive, What is the significance Time...

What is the significance Timescale directive? Defines time units and simulation precision (smallest increment). Syntax 'timescale TimeUnit / PrecisionUnit TimeUnit =

Explain open source software, Explain Open source software? Open Source...

Explain Open source software? Open Source Software is software for which the underlying programming code is available to the users so that they might be read it, make changes t

What are single stage and multistage networks, What are single stage and mu...

What are single stage and multistage networks? Compare the strengths and weaknesses of each. OR List the major difference in single stage, two stages and three stage Netw

How many types of stages include in process of data mining, How many types ...

How many types of stages include in process of data mining? The process of data mining comprised three stages as given below: a) The initial exploration b) Model buildin

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