First-order models -artificial intelligence, Computer Engineering

First-Order Models - Artificial intelligence:

We proposed first-order logic like good knowledge representation language rather than propositional logic because it is more expressive, so we may write more of our sentences in logic. So the sentences we want to apply inference andrewrites rules will include quantification. All of the rewrite rules we have seen so far may be used in propositional logic (and hence first-order logic). Now we consider rules in which rely on information regarding the quantifiers, so there are not available to an agent working with a propositional logic representation scheme.

Before we look at first-order inference rules we have to pause to consider what it means for such an inference rule to be sound. Previously we defined it as meaning the top entails the bottom: that any model of the former was a model of the latter. But first order logic introduces new syntactic elements (quantifiers, functions, constants, variables, and predicates) alongside the propositional connectives. It means we have to fully revise our definition of model, a notion of a 'possible world' that defines whether a sentence is  false ortrue in that world.

A propositional model was only an assignment of truth values to propositions. A first-order model is a pair (Δ, Θ) in contrast where

  • Δ is a domain, a non-empty set of 'objects', for example things which our first-order sentences are referring to.
  • Θ is an interpretation, a process for calculating the truth of sentences relative to Δ.

This appears very different from propositional logic. Luckily, everything we have discussed so far regarding deduction carries over into first-order logic when we use this new definition of model.

First-order logic lets us to talks regarding properties of objects, so the first task for our model (Δ, Θ) is to assign a meaning to the terms that represent objects. A ground term is any arrangement of constant and function symbols, and Θ maps each specific ground term to a specific object in Δ. This means that a ground term refers to a single particular object. The meaning of sub terms is always not dependent of the term they appear in.

The  specific  way  that  terms  are  mapped  to  objects  depends  on  the  model. Different models may define terms as referring to different things. Note down that although father (john) and jack are separate terms, they must both be mapped to the same object (say Jack) in Δ. That is, the 2 terms are syntactically different but (in this model) they are semantically the similar, for example, they both refer to the same thing!

Terms may also contain variables (for example father(X)) - these are non-ground terms. They do not refer to any particular object, and so our model cannot directly assign any single meaning to them. We will come back to what variables mean.

Posted Date: 10/2/2012 8:18:40 AM | Location : United States







Related Discussions:- First-order models -artificial intelligence, Assignment Help, Ask Question on First-order models -artificial intelligence, Get Answer, Expert's Help, First-order models -artificial intelligence Discussions

Write discussion on First-order models -artificial intelligence
Your posts are moderated
Related Questions
what isAdvantages of scan line algorithm, Computer Graphics?

what is Ambiguity in single inheritance

What is the working set of a process? The set of pages that are referred by the method in the last "n", references, where "n" is called the window of the working set of the pro

Q. VLSI Implementation of Control Unit? A main potential advantage of RISC is VLSI implementation of microprocessor. VLSI Technology has decreased the delays of transfer of inf

Execution of a program in CPU is completed employing different set of registers and their individual circuitry. As CPU registers are used for execution of interrupt service routine

Explain how a critical section avoids Race condition. To prevent Race Condition, concurrent processes should be synchronized. Data consistency needs that only one process m

For this project, we hope to use the basic idea of InfraRed (IR) communication for our television in ES103.  In ES103, we have a Sony large-screen television that we hope to commun

State about An active graphics device An active graphics device allows the user to communicate with the computer graphically. Generally, this implies that the user is supplyin

What is trivial file transfer protocol? Explain briefly? Trivial File Transfer Protocol (i.e. TFTP) is helpful for bootstrapping a hardware device which does not have a disk on

Determine the term- Files File maintenance is significant. Updating of files generally involves inserting, amending and deleting data. Example: A bank would amend data