Belief dynamics and defeasible argumentation in rational agents M. A. Falappa - A. J. García G. R. Simari Artificial Intelligence Research and Development Laboratory Department of Computer Science and Engineering Universidad Nacional del Sur - Argentina
23
Embed
Belief dynamics and defeasible argumentation in rational agents
Belief dynamics and defeasible argumentation in rational agents. M. A. Falappa - A. J. García G. R. Simari Artificial Intelligence Research and Development Laboratory Department of Computer Science and Engineering Universidad Nacional del Sur - Argentina. Motivation. - PowerPoint PPT Presentation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Belief dynamics and defeasible argumentation
in rational agents
M. A. Falappa - A. J. García
G. R. Simari
Artificial Intelligence Research and Development Laboratory
Department of Computer Science and Engineering
Universidad Nacional del Sur - Argentina
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 2
Motivation
• Use a kind of non-prioritized revision on defeasible logic programming (DeLP).
• Apply this kind of operator on the beliefs of an BDI agent.
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 3
Knowledge representation• The knowledge of an agent will be represented
by a defeasible logic program =(,). is a set of facts and strict rules.
– Facts are ground literals that could be negated by the use of strong negation “”.
– Strict rules are denoted as:
L0 L1, L2, …, Ln
where Li are ground literals.
is a set of defeasible rules denoted as:
L0 L1, L2, …, Ln
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 4
Defeasible rules• A defeasible rule is denoted as:
L0 L1, L2 ,…, Ln
L0 is a ground literal called the head and L1, …, Ln
are ground literals that form the body of the rule.
• This kind of rule is used to represent tentative information:
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 11
Belief Bases
There are two kinds of beliefs:• Explicit Beliefs: all the sentences in the belief
base.• Implicit Beliefs: all sentences derived from the
belief base.
The implicit beliefs are “explained” from more basic beliefs.
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 12
ExplanationsAn explanans justifies an explanandum.
Set of sentences A sentence
Properties [FKS02]:
• Deduction: A .• Consistency: It is not the case that A .• Minimality: There is no set A A such that A .• Informational Content: It is not the case that A.
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 13
Informational Content
This postulate avoids the following cases:
• Self-explanation:
{ } be an explanation of
• Redundancy:
{ , } be an explanation of
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 14
• We will define operators for revision with respect to an explanans (a set of sentences).
• The idea is the following:
– Instead of incorporating a sentence , call for an explanans A for .
– Add A to .– Eliminate all posible inconsistencies from
the result.
Revision by a set of sentences
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 15
Revision by a set of sentences
A Explanans for
A
( A)
Possiblyinconsistent
state
could not be accepted
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 16
Main ways of contractionPartial meet mode [AGM85]:
• Let be a set of sentences and be a sentence.
• Find all maximally subsets of failing to imply (-remainders), noted as .
• Select the “best” -remainders by a selection function .
• Intersect them.
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 17
Main ways of contraction
Kernel mode [Hansson94]:
• Let be a set of sentences and be a sentence.
• Find all minimally subsets of implying (-kernels), noted as .
• Cut the -kernels by an incision function .
• Give up the cut sentences from .
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 18
Revision by a Set of Sentences
Definition: Let and A be set of sentences, “” an external selection function for . The operator “” of partial meet revision by a set of sentences is defined as:
A = (( A) )
Definition: Let and A be set of sentences, “” an external incision function for . The operator “” of kernel revision by a set of sentences is defined as:
A = ( A) \ (( A) )
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 19
Revision on DeLP: definition
T+( ) = (positive transformation)
T– ( ) = (negative transformation)
Definition: The composed revision of (,) with respect to A is defined as (,)A= (,) such that = A and = where:
= {T+(): \ (A)} {T–(): \ (A)}
Falappa, García & Simari International Workshop on Non-Monotonic Reasoning 20
Revision on DeLP: an example
metal(hg)
metal(fe)
solid(X) metal(X)
liquid(X) solid(X)
solid(X) liquid(X)
= = { }
Then, we receive the following explanation for liquid(hg):