Kahn & Gorry's Time Specialist (Kahn & Gorry 1977)
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Transcript of Kahn & Gorry's Time Specialist (Kahn & Gorry 1977)
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.