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 socket inheritance, What is socket inheritance? Explain. Socke...

What is socket inheritance? Explain. Socket Inheritance: In a socket inheritance a reference count mechanism is utilized. Whenever a socket is first created, the system set

Explain intermediate representation, a. Explain Intermediate Representation...

a. Explain Intermediate Representation? What are the desirable properties of Intermediate Representation? b. Explain Grammar of a language. Identify the dissimilar classes of gr

What is visibility give uml notation, What is visibility give UML notation?...

What is visibility give UML notation? Visibility refers to the ability of a process to reference a feature from another class and has possible valued of public, private, protec

Rank the list elements in terms of distance, Q. Rank the list elements in t...

Q. Rank the list elements in terms of distance? Rank the list elements in terms of distance from each to last element in given linear linked list. A parallel algorithm for t

What is the meaning of rigging, Rigging is use for if we need to give anima...

Rigging is use for if we need to give animation for any object or character then we apply to character or object internal bone setting(like our bones).that is known as rigging. Whe

Multi-layer network architectures, Multi-Layer Network Architectures - Arti...

Multi-Layer Network Architectures - Artificial intelligence: Perceptrons have restricted scope in the type of concepts they may learn - they may just learn linearly separable f

How to define a filename in dos, Q. How to define a Filename in DOS? Ea...

Q. How to define a Filename in DOS? Each file is given a name so that it can be referred to later. This name is termed as Filename. The filename in DOS can be up to eight alpha

Transaction, Explain Shadow Copy Scheme in detail.

Explain Shadow Copy Scheme in detail.

Advantage of a numeric mailbox identifier, Does a numeric mailbox identifie...

Does a numeric mailbox identifier have any advantage over a mnemonic identifier? Explain. Several software systems permit the system administrator to select mailbox names, wher

How free-space is managed using bit vector implementation, How free-space i...

How free-space is managed using bit vector implementation? The free-space list is executed as a bit map or bit vector. Each block is shown by 1 bit. If the block is free, the b

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