Temporal Reasoning:Past, Present, and Future

Part I: Temporal Reasoning in Philosophy and Linguistics

Yuval Shahar

Stanford Medical Informatics

Time in Natural Language

From—

“Mr. Jones was alive after Dr. Smith operated on him”

Does it follow that—

“Dr. Smith operated on Mr. Jones before Mr. Jones was alive?”

Is Before the inverse of After?

Understanding a Narrative

• List all, find at least one, or prove the impossibility of a legal scenario for the following statements:– John had a headache after the treatment

– While receiving treatment, John read a paper

– before the headache, John experienced a visual aura

• One legitimate scenario (among many) is:– “John read the paper from the very beginning of the

treatment until some point before its end; after reading the paper, he experienced a visual aura that started during treatment and ended after it; then he had a headache.”

Paper Aura

Treatment Headache

Monitoring

Determine if an oncology patient’s record indicates a second episode that has been lasting for more than 3 weeks, of Grade II bone-marrow toxicity (as derived from the results of several different types of blood tests), due to a specific chemotherapy drug.

Planning and Execution

If the patient develops sever anemia for more than 2 weeks, reduce the chemotherapy dose by 25% for the next 3 weeks and in parallel monitor the hemoglobin level every day.

Display and Exploration of Time-Oriented Data

Timing is Everything :Applications of Temporal Reasoning

• Natural-language processing (e.g., story understanding)

• Planning (e.g., robot planning, therapy planning)

• Causal reasoning (e.g., diagnosis)

• Archeology (e.g., seriation)

• Psychology (e.g., developmental behavioral psychology)

• Scheduling (e.g., optimal ordering)

• Circuit design (e.g., sequential circuits)

• Software design (e.g., parallel processing, communication, verification)

• Other, not necessarily time-oriented, domains where interval algebra is useful, such as molecular biology (e.g., arrangement of DNA segments along a linear DNA chain) and evaluation of spatiotemporal traffic-flow patterns

A Temporal-Reasoning Task:Temporal Abstraction

• Input: time-stamped clinical data and relevant events

• Output: interval-based abstractions

• Identifies past and present trends and states

• Supports decisions based on temporal patterns “modify therapy if the patient has a second episode of Grade II bone-marrow toxicity lasting more than 3 weeks”

• Focuses on interpretation, rather than on forecasting

Temporal Abstraction:A Bone-Marrow Transplantation Example

.

•

0 4 0 02 0 01 0 05 0

•

1 0 0 0

2 0 0 0

( )

1 0 0 K

1 5 0 K( )

•••

• • • •

•

• •

•

••

G r a n u -lo c y tec o u n ts

• • •

•

T im e ( d a y s )

P la t e le tc o u n ts

P A Z p r o t o c o l

Uses of Temporal AbstractionsIn Medical Domains

• Planning therapy and monitoring patients over time

• Creating high-level summaries of time-oriented patient records

• Supporting explanation in medical decision-support systems

• Representing the intentions of therapy guidelines

• Visualization and exploration of time-oriented medical data

Temporal Reasoning Versus Temporal Maintenance

• Temporal reasoning supports inference tasks involving time-oriented data; often connected with artificial-intelligence methods

• Temporal data maintenance deals with storage and retrieval of data that has multiple temporal dimensions; often connected with database systems

• Both require temporal data modeling

Clinicaldecision-supportapplication

TM TR DB

Choices in Modeling Time

• What are the basic temporal primitives? Are they points, intervals, or events that create temporal references, such as BIRTH?

• Is time discrete or continuous?

• What is the meaning of Past, Present, and Future? In particular, what is the meaning of Now?

• What is the structure of time? Does time branch? Is the timeline linear, parallel, or circular?

• What do temporal relations mean? Is Before the antonym of After?

A Logical Interlude:First-Order Logic (FOL)(Predicate Calculus)

• Constants: Mr_Smith, Dr._Jones, anemia

• Variables: X, Y

• Functions: Address(X), Age(Y)

• Predicates: Diagnosis(X, anemia); Male(Y); Patient(Z)

• Negation: ¬Male(X); ¬Name(X, Smith)

• Connectors:

– Conjunction (AND): Patient(X) Male(X)

– Disjunction (OR): Doctor(X) Nurse(X)

– Logical implication: Female(X) ¬Male(X)

• Quantifiers:

– Universal quantifier: X (Patient(X) Doctor(X))

– Existential quantifier: Y (Patient(Y) Name(Y, Jones))

The Master Argument(Diodorus Chronus, 300 B.C.)

I. Everything that is past and true is necessary (what is past and true is necessary thereafter)

II. The impossible does not follow the possible (what is once possible does not become impossible)

=> Nothing is possible which is neither true nor will be true

=> every [present] possibility must be realized at some present or future time

=> logical determinism: what is necessary at any time must be necessary at all earlier times, a typical stoic conclusion

Prior's Tense Logic(1955)

• A modal logic of futurity, originally inspired by Diodorus

- Fp —> it will be the case that p

- Pp —> It was the case that p

- Gp —> it will always be the case that p ¬F¬p

- Hp —> it was always the case that p ¬P¬p

=> The modal (or "tenser") approach to time, as opposed to FOL • Example difference: for a "tenser," F(x) f(x) (x) Ff(x) !! But NOT for a "detenser," since these are equivalent in FOL

• On the other hand, FOL is a model theory for modal approaches

McTaggart’s Temporal Series(1908)

• The A series: The series of positions running from Past to Future

• The B Series: The series of positions running from Earlier to Later

=> Each temporal position has two aspects-Past, Present, or Future; and earlier than some or later than other positions

• The C series: The B series devoid of temporal direction

• McTaggart tried to show that the B series implies the A series, but that the A series is inconsistent, and thus time is unreal! The argument has been refuted several times since then

A Musical Interlude(modified from Anscombe, 1964)

• "Haydn was alive before Mozart was alive"

Does it follow that Mozart was alive after Hyden was alive??

• "Haydn was alive after Mozart died"

Does it follow that Mozart died before Haydn was alive??

=> BEFORE and AFTER are not strict converses of each other [note: after can be a converse of before, with proper definitions]

But: "Haydn was born before Mozart was born" Indeed, Mozart was born after Haydn was born.

=> BEFORE and AFTER are converses when they link events.

=> A taxonomy of verb-types by aspects

Reichenbach's Tenses(1947)

• There are just three times accounting for every tense:

- U [utterance time]

- R [reference Time]

- E [event time]

e.g., "I shall have gone:"

U before R & R after E

Assuming temporal adverbials attach to the reference time,this explains why "I did it yesterday" and "I did it today"or "I have done it today," but NOT "I have done it yesterday" (since R = U = now)

Bruce's Chronos System(1972)

• A formal model of temporal reference in natural language

• Generalizes Reichenbach's 3-point tense theory to n relations

• Defines 7 basic time-segment relations Ri: before, during, same-time, overlaps, after, contains, overlapped

• A tense is a n-ary relation on time intervals:

Ri (Si, Si+1) i= 1..n-1

where S1...Sn-2 are time points [S1 = U, Sn = E, S2...Sn-1 = R] Ri is a binary ordering relation on time segments Si, Si+1

e.g., "He will have sung" -> BA( S1,...S3 ) or BSA( S1,...S4)

The Chronos Architecture

User

Parser Generator

Control

Facts about events

Self updating

Theorem Prover

Rules of inference

Clock

Input Output“Natural Language”

Input Output“Formal Language”

A Chronus Example Run

(Did the time of the American war for independence overlap the articles of Confederation period *)

- Yes(When was the American war for independence *) - (In the past from 1775 to 1781)(The American revolutionary period was from 1750 to

1790)- (Information accepted)

(Is it true that the American revolutionary period contains the articles of Confederation period *)

- Yes

Chronos: Evaluation

• Only a prototype, examining a theory of natural language tenses

• No particular temporal network structure or search heuristics

• No attempt to understand the propositions involved

• A given symbol might or might not be a tense marker (context dependent)

e.g.: "He was to go" as the tense-logical PFp vs. an obligatory form

• A given tense marker might indicate different tenses (context dependent)

e.g.: "If the economic depression hasn't improved by the time Clinton runs for his next election, there will be a change of presidents"

where the present perfect and simple present have temporal references BA and B, rather than the A and S (as Chronos would parse them).