Representingactionsa ndtheenvironment

Representing actions and the environment: 

Representing actions and the environment

Representation issues: 

Representation issues If there are n properties of the world then there may be 2n states of the world. Actions often change the state of the world. How do we express the change in the state of the world due to an action? A simple table would need to have 2n rows and m columns, where m is the number of actions So how do we succinctly express the change in the state of the world due to an action? Lets analyze how we do it.

Some example agent domains: Travel Agent: 

Some example agent domains: Travel Agent Goal: Be in NYU, Building 1, Rm 232 tomorrow morning at 9 AM. Actions: Fluents (properties of the world): Describing the effect of actions on the world:

What we need?: 

What we need? A language in which we can express the effect of actions on the environment. A reasoning mechanism around this language using which we can ask questions regarding Correctness of plans/controls Making plans/controls

The language A: 

The language A Goal: A simple language to describe the effect of actions on the environment. Example: loading the gun causes the gun to be loaded. shooting causes the turkey to die if the gun is loaded. actions: load, shoot. fluents (binary variables that describe the environment): loaded, alive fluent literals: fluents and their negations : loaded, ~loaded, alive, ~ alive

Syntax of A: an example: 

Syntax of A: an example load causes loaded shoot causes ~alive if loaded Or shoot causes ~alive executable shoot if loaded General form to represent effect of actions Effect proposition: a causes f if p1, …, pn Executability Condition: executable a if q1, …, qm Domain Description: a set of effect propositions and a set of executability conditions

Syntax of A - cont.: 

Syntax of A - cont. What else do we need besides describing effect of actions on the environment? What (kind of reasoning) will an autonomous agent do with this knowledge? Observations! The turkey is initially alive. The turkey was observed to be dead after shooting. Useful in planning, knowledge assimilation. Planning from a complete initial situation: The gun is initially not loaded and the turkey is initially alive. How to achieve the state where the turkey is not alive? Conformant planning with possibly incomplete initial state: We don't know if the gun is initially loaded or not and the turkey is initially alive. How to achieve the state where the turkey is not alive? Knowledge assimilation: We don't know if the gun is initially loaded or not and the turkey is initially alive. We observe that the turkey is dead after shooting. What can we conclude more?

Syntax of A – Observation and Queries: 

Syntax of A – Observation and Queries Observation (O): f after a1, …, an. f was observed to be true after a1, …, an is executed in the initial situation. f would be true in the resulting state if a1, …, an were to be executed in the initial situation initially f Queries (Q): f after a1, …, an. Will f be true after executing a1, …, an in the initial situation? Would f be true if a1, …, an were executed in the initial situation? Entailment: (D,O) |= Q

Semantics of A – motivating examples: 

Semantics of A – motivating examples D1 = { load causes loaded; shoot causes ~alive if loaded } D2 = { load causes loaded; shoot causes ~alive; executable shoot if loaded} O1 = {initially ~ loaded; initially alive } O2 = {initially alive} O3 = = {initially alive; ~alive after load, shoot } Plan verification (hypothetical reasoning): (D1, O1) |= ~ alive after load, shoot? Simple planning: Find a such that (D1, O1) |= ~ alive after a? Conformant planning: Find a such that (D1, O2) ~ alive after a? Observation assimilation: (D1, O3) |= initially loaded? Exercise: Replace D1 by D2 in the above reasoning tasks.

Semantics of A0: lead-in to the definition of |= : 

Semantics of A0: lead-in to the definition of |= Domain descriptions in A0 do not have executability conditions. Our goal: To define (D, O) |= Q Lets first consider O such that it is of the form initially f Q1: What kind of information does such an O encode? Q2: What kind of information D encodes?