Temporal reasoning and Planning in Medicine

Temporal Reasoning:Past, Present, and Future

Part II: Temporal Reasoning in Computer Science/Artificial

Intelligence

Yuval Shahar, M.D., Ph.D.

Kahn & Gorry's Time Specialist(Kahn & Gorry 1977)

• Knowledgable about time — a domain-independent module

• Isolates the temporal-reasoning element — not a temporal logic

• Specializes in organizing temporal aspects of knowledge

• Uses three different organization schemes, controlled by the user:

- organizing by dates on a date line

- organizing by special reference events (e.g., birth, now)

- organizing by before/after chains, for an event sequence

• Maintains consistency of the data base

• Answers questions of the type "what," "when," using a fetcher

The Time Specialist Architecture

User

Memory

Inference

methods

Fact

organizer

Error

corrector

Consistency

checker

Questions

Questions

FactsQuestionsCorrections Facts

Facts

New factsDoubted facts

Doubted facts

The Situation Calculus(McCarthy 1957; McCarthy and Hayes, 1969)

• Represents actions and their effects on the world

• The world is represented as a set of states

• Actions are functions that map states to states:

s True(s, closed_door) True(Result (open, s), Open_Door)

• On(Block1, Block2) is not a predicate; On is a function that returns all states in which Block1 is on Block2; thus, True(s,Open_Door) means that s is a member of the set of states in which the door is open

• Used for multiple tasks, especially planning

• Major problems:– Concurrent actions cannot be represented

– No duration of actions or delayed effects (Open creates result immediately)

– Other problems that are not specific to the situation calculus

Hayes’ Histories(1985)

• A history is an entity that incorporates time and space

• An object O in a situation s, represented as O@S, is the intersection of the situation with the object’s history

• Permanent locations are bound spatially, but are restricted temporally

• Situations are unbound spatially, but are limited temporally by surrounding events

• Most objects are between these two extremes

• Events are instantaneous

• Episodes have a duration

=> The history of an object can be described over time

Qualitative Physics

• Introduced by Hayes in his Naïve Physics Manifesto (1978, 1985), in which he argued for formalizing and axiomatizing a sizable portion of the real world (also known as commonsense reasoning)

• Taken up by the Qualitative Physics (QP) branch of the Artificial Intelligence research community– Circuits were described as components and connections (De Kleer

and Brown, 1985)

– Qualitative Process Theory reasoned about active processes such as boiling water (Forbus 1984)

– A general qualitative simulation framework (QSIM) was developed and implemented in software (Kuipers, 1986)

– A methodology was developed to describe and detect cycles in repeating processes (Weld, 1986)

Time in Qualitative Physics

• QP approaches usually have no explicit representation of time

– Instead, they refer to a set of key states (landmarks) and a transition function that changes a state into another state

• Typically, even when time is modeled, it is used only implicitly

– Time is often an independent variable in qualitative equations, rather than a first-class citizen with its own properties

Kowalsky & Sergot's Event Calculus

(1986)• Developed for updating databases and for narrative understanding

• Based on the notion of an event and its descriptions (relationships)

• Relationships are ultimately over time points after(e) = the period of time started by event e

• Udates can only add; deletions add new information about the end of the period of time over which the old relationship holds

• Uses nonmonotonic, default reasoning since relations change as new information arrives (a new event can signal the end of an old one)

• Allows partial description of events, using semantic cases

• Defined and interpreted as Horn clauses in Prolog: Assigned-to(Person, Project, after(Event)) IF employed-on (Person, Project, Event)

Allen's Temporal Logic(1981–84)

• Intended to support natural-language understanding and planning

• Time primitives are temporal intervals - no instantaneous events

• No branching into the future or the past

• 13 basic (binary) interval relations [b,a,eq,o,oi,s,si,f,fi,d,di,m,mi], such as Before and After; six are inverses of the other six

• Supported by a transitivity table that defined the conjunction of any two relations and a sound but incomplete algorithm that propagates efficiently (in O(n3)) the results of applying the relations

• All 13 relations can be expressed using meet [Allen & Hayes 85]; Before (X, Y) Z , (meets(X, Z) (meets (Z, Y))

X Z Y

Allen’s 13 Temporal RelationsA

B

A

B

A

B

A

B

A

B

A

B

A

B

A FINISHES B

B is FINISHED by A

A is BEFORE B

B is AFTER A

A MEETS B

B is MET by A

A OVERLAPS B

B is OVERLAPPED by A

A STARTS B

B is STARTED by A

A is EQUAL to B

B is EQUAL to A

A DURING B

B CONTAINS A

Allen’s Temporal Ontology

• Properties hold over every subinterval of an interval

—> Holds(p, T) e.g., "Patient1's skin was blue throughout sunday"

• Events hold only over an interval and not over any subinterval of it [note that they are not identified with a set of intervals]

—> Occurs(e, T) e.g., "patient2 broke a leg at 5pm"

• Processes hold over some subintervals of the interval they occur in

—> Occuring(p, T) e.g., "patient3 is chasing the nurse"

McDermott's Temporal Logic(1982)

• Goals: to model causality, continuous change and planning

• Time primitives are points

• Time is continuous — the time line is the set of real numbers

• States Si are instantaneous shots of the world with an order-preserving date function that maps them into time points

• A fact such as (On A B) is the set of states where A is on B, and are represented as (T s p) (the proposition p is true in state s; or: s is a member of the set of states in which p is true)

• An event e is the set of intervals (pairs of states) during which it happens, and is represented as (Occur S1 S2 e)

McDermott’s Chronicles

• States are partially ordered and branching into the future, but totally ordered in the past (known past, indeterminate future)

• Each maximal linear path in the state tree is a chronicle

• A chronicle is a complete history of the world, a totally ordered set of states, extending to the indefinite past and future

Shoham's Temporal Logic(1987)

• Time primitives are points

• Propositions are interpreted over intervals

• Reified first-order logic: TRUE(t1, t2, color(house17, red)),

- rejects the simple FOL approach: color( t1, t2, house17, red) which does not grant time any special status - rejects the modal approach: M, t1, t2,color(house17, red) which can be subsumed by reified FOL

• Provides clear semantics to a temporal formalism, without any of the particular commitments made by Allen or McDermott (such as by distinguishing facts from events)

Shoham’s Temporal-Proposition Types

• Relate the truth of the proposition over one time interval to the truth of the proposition over other time intervals– Downward-hereditary: Whenever it holds over an inteval it holds

over all its subintervals (John was in a coma on Tuesday)– Upward-hereditary: Whenever it holds for all proper

subintervals of an interval, it holds over the interval (John received an infusion of insulin at the rate of 2 units per minute)

– Gestalt: Whenever it holds over an interval, it never holds over a subinterval of that interval (John was in a coma for 2 weeks)

– Concatenable: Whenever it holds over two consecutive intervals, it holds over their union (John had high blood pressure)

– Solid: Whenever it holds over an interval, it never holds over an overlapping interval (e.g., John received a full course of chemotherapy from start to end)

=> Allen's properties are downward-hereditary propositions; Allen's and McDermott's events are gestalt, solid or both.