Truth management system

Presentation on Truth Maintenance System in AI

Group Members:

Sl. No Name ID1 Najmul Hasan 1109013

2 Noormohammed 1109009

3 Md. Kamrul Hasan 1109010

4 Mesbah Uddin 1109011

What is TMS? A TMS deals with uncertainty by permitting new knowledge to replace

old knowledge which is believed to be outdated or erroneous.

A Truth Maintenance System (TMS) is a Problem Solver module

responsible for:

Enforcing logical relations among beliefs.

Generating explanations for conclusions.

Finding solutions to search problems

Supporting default reasoning.

Identifying causes for failure and recover from inconsistencies.

1. Enforcement of logical relations AI problem -> search. Search utilizes assumptions. Assumptions change. Changing assumptions -> updating consequences of beliefs. TMS: mechanism to maintain and update relations among beliefs.

(Every AI problem which is not completely specified requires search. Search utilizes assumptions, which may eventually change. Changing assumptions requires updating consequences of beliefs. Re-derivation of those consequences is most often not desirable, therefore we need a mechanism to maintain and update relations among beliefs.)

1. Enforcement of logical relationsExample: If (ICT-601) and (math-218) then (ICT-570).

If (ICT-570) and (ICT) then (TMS).

If (TMS) then (AI-experience).

The following are relations among beliefs:

(AI-experience) if (TMS).

(TMS) if (ICT-570), (ICT).

(ICT-570) if (ICT-501), (math-218) Beliefs are propositional variables TMS is a mechanism for processing large collections of logical relations on propositional

variables.

2. Generation of explanations Solving problems is what Problem Solvers do.

However, often solutions are not enough. The PS is expected to provide an explanation TMS uses cached inferences for that aim. TMS is efficient:

Generating cached inferences once is more beneficial than running inference rules that have generated these inferences more than once.

2. Generation of explanationsExample:

Q: Shall I have an AI experience after completing the ICT program?

A: Yes, because of the TMS course.

Q: What do I need to take a TMS course?

A: ICT-611 and AI and Expert system. There are different types of TMSs that provide different ways of

explaining conclusions (JTMS vs ATMS). In this example, explaining conclusions in terms of their

immediate predecessors works much better.(Solving problems is what PSs do. However, often solutions are not enough -the PS is expected to provide an explanation for the proposed solution so that the user can identify the cause of a problem if something goes wrong. To provide explanations, a TMS uses cached inferences.)

3. Finding solutions to search problems A

B E C D

Color the nodes: red (1), green (2) yellow (3). Adjacent nodes are of different colors. The set of constraints describe this problem:A1 or A2 or A3 not (A1 and B1) not (A3 and C3) not (D2 and E2)B1 or B2 or B3 not (A2 and B2) not (B1 and D1) not (D3 and E3)C1 or C2 or C2 not (A3 and B3) not (B2 and D2) not (C1 and E1)D1 or D2 or D3 not (A1 and C1) not (B3 and D3) not (C2 and E2)E1 or E2 or E2 not (A2 and C2) not (D1 and E1) not (C3 and E3)

(Assume you want to color the nodes so that every node is red, or green, or yellow, and adjacent nodes are of different colors. Let "1" means "red", "2“ means "green", and "3" means "yellow". Then, the following set of constraints describe this problem

To find a solution we can use search:

3. Finding solutions to search problem

A is red A is green A is yellow

B is red B is green B is yellow

C is green C is redC is yellow

D is red D is yellow D is green

E is red E is green E is yellow

4. Default reasoning and TMS

PS must make conclusions based on incomplete information.

“Closed-World Assumption” (CWA) X is true unless there is an evidence to the contrary. CWA helps us limit the underlying search space. The reasoning scheme that supports CWA is called

“default (or non-monotonic) reasoning”.

4. Default reasoning and TMSMany real-world problems cannot be completely specified. That is, the PS must make conclusions based on incomplete information. Typically the assumption under which such conclusions are drawn is that X is true unless there is an evidence to the contrary. This is known as the “Closed-World Assumption” (CWA). Notice that the CWA helps us limit the underlying search space by assuming only a certain choice and ignoring the others. The reasoning scheme that utilizes this assumption is called “default (or non-monotonic) reasoning”. Example: Consider the following knowledge base

Bird(tom) and not Abnormal(tom) Can_fly(tom)

Penguin(tom) Abnormal(tom)

Ostrich(tom) Abnormal(tom)

Bird(tom)

Under the CWA, we assume not Abnormal(tom) (because there is no evidence that Tom is abnormal). Therefore, we can derive can_fly(tom).

Non-monotonic TMS supports this type of reasoning.

5. Identifying causes for failures and recovering from inconsistencies

Inconsistencies among beliefs in the KB are always possible:

wrong data (example: “Outside temperature is 320 degrees.”) Impossible constraints (example: Big-house and Cheap-house and Nice-house).

TMS maintains help identify the reason for an inconsistency Non-monotonic inference. PS is forced to “jump” to a conclusion, because of

the lack of information, or lack of time to derive the conclusion.

“dependency-directed backtracking” allows the TMS to recover.

Noormohammed

TMS applications Constraint Satisfaction Problems (CSP)

Set of variables

Domain over each variable

Constraints between variables’ domain

Goal: find “solution”: assignments to the variables that satisfy the constraints

Scenario and Planning Problems Find a path of state transitions lead from initial to final states. (games,

strategies).

TMS – identifies of applicable rules.

Problem Solver Architecture

Inference engine

TMS

Poblem solver

Knowledge base

Tell

Ask

The TMS / PS relationship is the following:

How the TMS and the PS communicate? The PS works with:

assertions (facts, beliefs, conclusions, hypotheses) inference rules procedures

Each one of these is assigned a TMS node. Example: N1: (rule (student ?x) (assert (and (underpaid ?x) (overworked ?x)))) N2: (student Bob)

Given N1 and N2, the PS can infer N3: (and (underpaid Bob) (overworked Bob))

PS treats nodes as logical formulas, While TMS treats nodes as propositional variables.

TMS Nodes Different types of TMS support types of nodes:

Premise nodes. These are always true.

Datum nodes. These are either a currently assumed or IE derived belief.

Justification nodes. These are the belief supports, consisting of supporting antecedent node links and a consequent node link.

Assumption nodes. PS believes no matter whether or not they are supported by the existing evidence.

Node has a label associated with it. The contents and the structure of the label depends on the type of TMS.

Other properties are node type (premise, assumption, etc.), node support (justifications, antecedents), node consequences, etc.

TMS Nodes Belief Network node meanings

Premises

Assumptions

Datum

Justifications

TMS justifications If N3, is created by the PS, it reports to the TMS together with

the fact that it follows from N1, N2. justification:

(N3 N2 N1)

Here N3 is called the consequent, N1 and N2 are the antecedents of the justification.

Justifications record relations among beliefs or explaining consequents and identifying causes for inconsistencies.

The general format of justifications is the following:

(<consequent> <antecedents>)

Propositional specification of a TMS As we have already seen, TMS nodes are propositional variables.

Therefore, we can view TMS justifications as propositional formulas (implications) of the form:

N1 & N2 & … & Ni Nj

Here N1, N2, …, Ni, Nj are positive literals, therefore this implication is a Horn formula.

TMS can be viewed as a set of Horn formulas

PS / TMS interaction

Responsibilities of the PS:

1. Adds assertions and justifications.

2. Makes premises and assumptions.

3. Retracts assumptions.

4. Provides advise on handling contradictions

Responsibilities of the TMS:

1. Cashes beliefs and consequences and maintains labels.

2. Detects contradictions.

3. Performs belief revision.4. Generates explanations.

Md. Kamrul Hasan

Families of TMSs

There are several families of TMSs. Only two is defined here:

1. Justification Based TMS

2. Assumption based TMS

Justification-based TMS

Justifications are used for: Belief update purpose, when belief state of

a node changes. Handle contradiction:

1. Justification is added to the dependency-directed backtracking system

2. Then search through the dependency network for the assumptions of the contradiction

3. Contradiction is removed.

Justification-based TMS A justification contains inlist and outlist for a justified node to

be believed:

inlist – a set of nodes that must be in

outlist – a set of nodes that must be out

Syntax: {(inlist),(outlist)}

Premises hold universally: empty in and out

Only one context includes the set of assumptions currently believed.

Justification-based TMS – Example

Propositions: Justifications:

A: Temperature>=25 {(),(B)}

B: Temperature< 25

C: Not raining {(),(D)}

D: Raining

E: Day {(),(F)}

F: Night

PS concludes “nice weather” from A and C

At the beginning Mak believes that A ,C and E




B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night

G: Nice weather {(A,C),()}New node in the JTMS




B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night

G: Nice weather {(A,C),()}

PS concludes “swim” from E and G




B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night


H: Swim {(E,G),()}

Justification-based TMS – ExamplePropositions: Justifications:


B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night


H: Swim {(E,G),()}

I: Contradiction {(C),()}

Dependency-directed backtracking system

PS provides a contradiction and the JTMS makes dependency-directed backtracking in order to infer that C caused to the contradiction. Therefore a TMS contradiction node is added and C is in its inlist which means C supports the contradiction


A: Temperature>=25 {(),(B)}B: Temperature< 25C: Not raining {(),(D)}D: RainingE: Day {(),(F)}F: Night

G: Nice weather {(A,C),()}H: Swim {(E,G),()}

I: Contradiction {(C),()}X: Handle {(),()} //premise

D: Raining {(X),()}

Context: {(A,D,E),(B,C,F,G,H,I)}

The backtracking finds D in the outlist of C and so D is justified by the contradiction of C.In order to solve the contradiction JTMS add the premise X as the inlist of D to make it assumed



B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night


H: Swim {(E,G),()}


X: Handle {(),()} //premise

D: Raining {(X),()}

J: Read {(D,E),()}

K: Contradiction {(J),()} //becomes tired

Dependency-directed backtracking system PS provides read as justified by

D and E After a while it became tired and so stopped to read, and the PS produced a contradiction to J. The backtracking finds the assumption E as faulty (because E is antecedent of J and D is supported by premise X in the inlist which is always true)



B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night


H: Swim {(E,G),()}



D: Raining {(X),()}

J: Read {(D,E),()}


F: Night {(X),()}

Context: {(A,D,F),(B,C,E,G,H,I,J,K)}

Then node F is added since it backtracked from the outlist of the contradiction E, and node F is justified.



B: Temperature< 25


D: Raining

E: Day {(),(F)}

F: Night


H: Swim {(E,G),()}



D: Raining {(X),()}

J: Read {(D,E),()}


F: Night {(X),()}

L: Sleep {(F),()}

The PS provides L as consequence of F

Mesbah Uddin

Assumption-based TMS ATMS is a general search – control

mechanism, that can be coupled with domain-specific problem to solve a wide range of problem

Start with a JTMSLabel become more complex than: in, out

ATMS data structuresAssumptionEnvironmentsLabels

Justifications Justifications is a relationships among

assumptions and nodes

1 l1 & l2 & K & ln n

2 l1 & l2 & K & ln

where:1 – truth of the node2 - inconsistensy

New Definitions

Environments = set of assumptionLabel = set of environments

Type of labels

Sound - All assumptions in any environment within the label of a nodebeing true is a sufficient condition to derive that node:

Consistent - No environment in the label of a node, other than the nogood node, describes an impossible world:

Minimal - The label does not contain possible worlds that are less general than one of the other possible worlds it contains (i.e. environments that are supersets of other environments in the label):

Complete - The label of each node, other than the nogood node, describes all possible worlds in which that node can be inferred:

Conclusions JTMS is used to maintain well fondness and assumption

based TMS (ATMS) for coherence No possible to tell which TMS is the best without analysing

the problem at hand and the resources available TMS in general handle knowledge, updates and revisions

efficiently TMS can be used to speed up the analysis of multiple

hypothetical situations.

Truth management system

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