The Telic\Atelic Distinction in Temporal Databases Paolo Terenziani Institute of Computer Science, DISIT, Univ. Piemonte Orientale “A. Avogadro”, Viale Teresa Michel 11, Alessandria, Italy Acknowledgements: - R.T. Snodgrass - A. Bottrighi, V. Khatri, G. Molino, S. Ram, M.Torchio - L. Lesmo, P. Torasso ER 2012 – ECDM-NoCoDA Workshop – October 15 th, Florence

The Telic\Atelic Distinction in Temporal Databases Summary: - Telic\atelic dichotomy (Linguistics) - (Data) semantics of relational temporal databases -The impact of the dichotomy on TDBs - New data model (semantics) - New query language (semantics: relational algebra) - Extensions to SQL & implementations - Conceptual modeling - Conclusions & open issues

The Telic\Atelic Distinction Aristotle’s “Categories” Telic facts: facts with a goal or culmination (e.g., John slept) Atelic facts: facts without goal\culmination (e.g., John build a house) (in Greek, “telos”=“goal”, “a” as a prefix indicates negation) Studied\used in -Philosophy - Linguistics - Cognitive Science … - Logics, Artificial Intelligence

The Telic\Atelic Distinction Deeply rooted in the Western culture E.g., from Cognitive studies: the aktionsart distinctions (and, in particular, the telic/atelic distinction) play a fundamental role in the acquisition of verbal paradigms by children: -[Bloom et al. 1980]: English, -[Bronckart & Sinclair, 1973]: French, -[Aksu, 1978]: Turkish.

The Telic\Atelic Distinction Moens and Steedman: “Effective exchange of information between people and machines is easier if the data structures that are used to organize the information in the machine correspond in a natural way to the conceptual structures people use to organize the same information” WHY SHOULD WE CARE? … BUT ALSO “MORE PRACTICAL” REASONS (current TDBs cannot cope correctly with telic facts!!)

The Telic\Atelic Distinction in Linguistics Linguistic sentences can be classified into different aktionsart classes according to their linguistic behavior and to their semantic properties E.g., [Vendler, 1967] Activities (e.g., “John slept”) Accomplishments (e.g., “John built a house”) Achievements (e.g., “John reached the top of the mountain”) States (e.g., “John had fever”)

The Telic\Atelic Distinction in Linguistics Different linguistic behavior E.g., progressive form Activities (e.g., “John was sleeping”) Accomplishments (e.g., “John was building a house”) Achievements (e.g., “John was reaching the top”) States (e.g., “John was having fever”)

The Telic\Atelic Distinction in Linguistics Semantic properties E.g., [Dowty, 1986] states vs. accomplishments: (1) A sentence  is stative if it follows from the truth of  at an interval I that  is true at all subintervals of I (e.g., if John was asleep from 1:00 to 2:00 PM, then he was asleep at all subintervals of this interval: be asleep is a stative). (2) A sentence  is an accomplishment/achievement (or kinesis) if it follows from the truth of  at an interval I that  is false at all subintervals of I (e.g., if John built a house in exactly the interval from September 1 until June 1, then it is false that he built a house in any subinterval of this interval: building a house is an accomplishment/achievement)

The Telic\Atelic Distinction in Linguistics Semantic properties Property 1 of states (and activities): downward inheritance. Property 2 of states (and activities): upward inheritance. E.g., if John was asleep from1:00 to 2:00 and from 2:00 to 3:00, then he was asleep from 1:00 to 3:00 NOTICE: neither Property 1 nor Property 2 holds for TELIC sentences (accomplishments)

The Telic\Atelic Distinction in Linguistics Language is FLEXIBLE “Basic” sentences can be classified as activities, accomplishments, achievements, and states Languages provides linguistic tools to switch from one class to the other [Verkuyl], [Moens & Steedman] e.g., when applied to an accomplishment, the progressive form converts it into an activity, since it strips out its culmination (i)“John built a house” is TELIC (ii)“John was building a house” is ATELIC (indeed, the culmination is not implied by (ii))

The Telic\Atelic Distinction IMPACT ON TEMPORAL RELATIONAL DBs Definition (Telic\Atelic facts). Atelic facts (data) are facts (data) for which both downward and upward inheritance hold; Telic facts are facts for which neither downward nor upward inheritance hold.

The Telic\Atelic Distinction IMPACT ON TEMPORAL RELATIONAL DBs three distinctions: (1)Representation versus semantics of the language (concrete vs. abstract databases [Chomicki, 1994]) (2)Data language versus query language. (3)Data semantics versus query semantics

DATA SEMANTICS BCDM (Bitemporal Conceptual Data Model [Jensen & Snodgrass, 96]) Temporal Domains - Time is linear and totally ordered - Chronons are the basic time unit - Time domains are isomorphic to subsets of the domain of Natural numbers D VT = {t 1,t 2, …, t k }(valid time) D TT = {t’ 1,t’ 2, …, t’ h }  {UC} (transaction time) D TT  D VT (bitemporal chronons)

BCDM Data Attribute names: D A ={A 1, A 2, …, A n } Attribute domains D D ={D 1, D 2, …, D n } Schema of a bitemporal relation: R = A i1, A i2, …, A ij T Domain of a bitemporal relation: D i1  D i2  …  D ij  D TT  D VT Tuple of a relation r(R): x = (a 1, a 2, …, a j | t B )

BCDM Example. Relation Employee with Schema: (name,salary,T) “Andrea was earning 60K at valid times 10, 11, 12” Such a tuple has been inserted into Employee at time 12, and is current now (say now=13)” (Andrea, 60k | {(12,10), (12,11), (12,12),(13,10), (13,11), (13,12), ……}) VT TT

BCDM Example. Relation Employee with Schema: (name,salary,T) “Andrea was earning 60K at valid times 10, 11, 12 Such a tuple has been inserted into Employee at time 12, and is current now (say now=13)” (Andrea, 60k | {(12,10), (12,11), (12,12),(13,10), (13,11), (13,12), (UC,10), (UC,11), (UC,12)}) VT TT UC

BCDM Bitemporal relation: set of bitemporal tuples. Constraint: Value equivalent tuples are not allowed. (Bitemporal) DB: set of (bitemporal) relations

BCDM Data Semantics (another viewpoint) NameSalaryT Andrea60K{(12,10), (12,11), (12,12),(13,10), (13,11), (13,12), (UC,10), (UC,11), (UC,12)} John50K{(12,12),(12, 13)} (12,10)  { } (12,11)  { } (12,12)  {, } (12,13)  { } (13,10)  { } (13,11)  { } …….. (UC,12)  { }

BCDM HENCEFORTH: focus on VALID TIME NameSalaryT Andrea60K{10,11,12} John50K{12,13} 10  { } 11  { } 12  {, } 13  { }

BCDM PROPERTIES Consistent extension (of “classical” SQL DB) A temporal DB is a set of “classical” DBs, one for each bitemporal chronon Uniqueness of representation (from the constraint about value equivalent tuples)

BCDM & al. POINT-BASED Data Semantics A temporal database is a function from time points to a standard (non-temporal) database “SNAPSHOT semantics” Artificial Intelligence \ logics: the truth of facts is evaluated at points in time

BCDM QUERY semantics r 1  B r 2 = {z | (∃x  r 1 ∃y  r 2 x[A]=y[A]=z[A] ∧ z[T]=x[T]  y[T])  (∃x  r 1 x[A]=z[A] ∧ (  ∃y  r 2 y[A]=z[A]) ∧ z[T]=x[T])  (∃y  r 2 y[A]=z[A] ∧ (  ∃x  r 1 x[A]=z[A]) ∧ z[T]=y[T])} Algebraic Operators (E.g. Union) - No value-equivalent tuple generated (uniqueness of representation!) - Coalescing!

BCDM Reducibility rTrT ρ t T (r T ) ρtTρtT op T (r T ) op T op op(ρ t T (r T )) ρtTρtT ρ t T (op T (r T )) =

An example of implementation: TSQL2 (Snodgrass et al., 1995) Temporal attribute T  four temporal attributes (TT S, TT E, VT S, VT E ) Attribute value: a timestamp or UC Bitemporal tuple: A 1,….A n | TT S, TT E, VT S, VT E Bitemporal relation: set of bitemporal tuples

An example of implementation: TSQL2 (Snodgrass et al., 1995) NameSalaryT Andrea60K{10,11,12} John50K{12} NameSalaryVT S VT E Andrea60K1012 John50K1213 SEMANTICS BCDM TSQL2 10  { } 11  { } 12  {, } 13  { }

BCDM (TSQL2 & al.) vs. TELIC\ATELIC NameSalaryVT S VT E Andrea60K1012 SEMANTICS TSQL2 10  { } 11  { } 12  { } Downward inheritance:  ([10,12])   (10)   (11)   (12)

BCDM (TSQL2 & al.) vs. TELIC\ATELIC SEMANTICS TSQL2 10  { } 11  { } 12  { } 13  { } Upward inheritance:  ([10,11])   ([12,13])   ([10,11]  [12,13]) NameSalaryVT S VT E Andrea60K1011 Andrea60K1213

BCDM (TSQL2 & al.) vs. TELIC\ATELIC Current temporal databases adopt BCDM semantics Naturally support Upward and Downward inheritance Naturally support ATELIC facts (data) WHAT ABOUT TELIC FACTS (DATA) ?

TELIC FACTS & BCDM (point-based) semantics E.g. Sue had an administration of 500 mg of cyclophosphamide (a cancer drug) starting at 1 and ending at 3 (inclusive) 1  { } 2  { } 3  { } Downward inheritance is (erroneously) enforced! How many administrations? What is their duration? How many mg. administered?

TELIC FACTS & BCDM (point-based) semantics E.g. Sue had - an administration of 500 mg of cyclophosphamide starting at 1 and ending at 3 (inclusive), and - an administration of 500 mg of cyclophosphamide at 4 1  { } 2  { } 3  { } 4  { } Upward inheritance is (erroneously) enforced! How many administrations? What is their duration? How many mg. administered?

TELIC FACTS & BCDM (point-based) semantics As well known in Linguistics (and Artificial Intelligence, Logics) 1  { } 2  { } 3  { } 4  { } POINT-BASED SEMANTICS IS NOT EXPRESSIVE ENOUGH TO COPE WITH TELIC FACTS (DATA)

SYNTAX vs. SEMANTICS of data For instance, TSQL2 uses time intervals in the representation NOTICE: this discussion is INDEPENDENT OF THE IMPLEMENTATION (representation syntax) NameDrugQuantityVT S VT E Suecyclophosphamide50013 Suecyclophosphamide50044

SYNTAX vs. SEMANTICS of data 1  { } 2  { } 3  { } 4  { } But they are merely a compact representation for a set of point, since the semantics is

SYNTAX vs. SEMANTICS of data 1  { } 2  { } 3  { } 4  { } Needless to remember that … Answers to query must be provided on the basis of the SEMANTICS of data (independently of the representation syntax) How many administrations? What is their duration? How many mg. administered?

TELIC FACTS & BCDM (point-based) semantics As predicted, e.g., by the Linguistic literature POINT-BASED (snapshot, BCDM, …) SEMANTICS IS NOT ADEQUATE (expressive enough) TO COPE WITH TELIC FACTS INTERVAL-BASED SEMANTICS IS NEEDED !!

SEMANTICS for TELIC FACTS E.g. Sue had - an administration of 500 mg of cyclophosphamide starting at 1 and ending at 3 (inclusive), and - an administration of 500 mg of cyclophosphamide at 4 [1,3]  { } [4,4]  { } INTERVAL-BASED SEMANTICS: function from INTERVALS to facts

SEMANTICS for TELIC FACTS: INTERVAL-BASED SEMANTICS INTERVALS ARE PRIMITIVE AND ATOMIC NOTIONS (i.e., NOT A NOTATION FOR A SET OF TIME POINTS !!!)

SEMANTICS for TELIC FACTS: INTERVAL-BASED SEMANTICS DiSIT has -A 50K contract with IBM from 1 to 12 -A 50K contract with IBM from 7 to 18 [1,12]  { } [7,18]  { }

INTERVAL-BASED SEMANTICS vs. TELIC\ATELIC NO downward inheritance:  ([1,3]) ↛  (1)  ([1,3]) ↛  (2)  ([1,3]) ↛  (3) [1,3]  { } [4,4]  { } Does not imply (mean) that Sue had a (complete) cyclophosphamide administration, e.g., at 2 The administration was exactly from 1 to 3 (and nowhere else)

INTERVAL-BASED SEMANTICS vs. TELIC\ATELIC NO upward inheritance:  ([1,3])   ([4,4]) ↛  ([1,4]) [1,3]  { } [4,4]  { } Does not imply (mean) that Sue had a (complete) cyclophosphamide administration from 1 to 4 She had two distinct administrations!

(DATA) SEMANTICS FOR TEMPORAL DATABASES Both ATELIC and TELIC facts exist [Aristotle] … POINT-BASED semantics is needed for ATELIC facts INTERVAL-BASED semantics is needed for TELIC facts Two-sorted data model, where - Atelic relations have a POINT-BASED semantics - Telic relations have an INTERVAL-BASED semantics (independently of the chosen implementation\representation) P. Terenziani, Proc. TIME’00, pp , P. Terenziani, R.T. Snodgrass, IEEE TKDE 16(5), pp , 2004.

QUERY SEMANTICS (ALGEBRA) Queries must operate on: -Atelic relations - Telic relations - Telic and Atelic relations together From Natural Language: - Flexibility is needed (conversion from\to telic\atelic)

ATELIC ALGEBRA r 1  A r 2 = {z | (∃x  r 1 ∃y  r 2 x[A]=y[A]=z[A] ∧ z[T]=x[T]  y[T])  (∃x  r 1 x[A]=z[A] ∧ (  ∃y  r 2 y[A]=z[A]) ∧ z[T]=x[T])  (∃y  r 2 y[A]=z[A] ∧ (  ∃x  r 1 x[A]=z[A]) ∧ z[T]=y[T])} e.g., BCDM Union between atelic relations Standard union between two sets of time points

ATELIC ALGEBRA 10  { } 11  { } 12  { } 13  { } NameSalaryT Andrea60K{10,11} UNION supports upward inheritance (COALESCING) NameSalaryT Andrea60K{12,13} NameSalaryT Andrea60K{10,11,12,13} 12  { } 13  { } 10  { } 11  { } AA

TELIC ALGEBRA r 1  T r 2 = {z | (∃x  r 1 ∃y  r 2 x[A]=y[A]=z[A] ∧ z[T]=x[T]  y[T])  (∃x  r 1 x[A]=z[A] ∧ (  ∃y  r 2 y[A]=z[A]) ∧ z[T]=x[T])  (∃y  r 2 y[A]=z[A] ∧ (  ∃x  r 1 x[A]=z[A]) ∧ z[T]=y[T])} Terenziani & Snodgrass, TKDE 2004 Union between telic relations Standard union between two sets of time intervals E.g., {[10,15], [20,25]}  {[5,30], [20,40]} = {[5,30],[10,15], [20,25], [20,40]}

TELIC ALGEBRA TELIC UNION does not support upward inheritance TT NameDrugQuant.T SueCycloph.500[1,3] [1,3]  { } [4,4]  { } NameDrugQuant.T SueCycloph.500[1,3] SueCycloph.500[4,4] NameDrugQuant.T SueCycloph.500[4,4] [4,4]  { } [1,3]  { }

TELIC ALGEBRA In principle: a polymorphic adaptation of a “consensus” atelic algebra (e.g., BCDM algebra) where set operators on temporal elements operate on sets of time intervals instead that on sets of time points However, both commonsense and semantic restrictions might\should be considered in the definition of both atelic and telic operators

ATELIC\TELIC ALGEBRA Ex.1TELIC CARTESIAN PRODUCT Atelic Cartesian Product involves the INTERSECTION of temporal elements (i.e., of sets of time points - semantic level) Its polymorphic TELIC adaptation would involve the INTERSECTION of sets of time intervals, giving in output only common time intervals e.g., {[10,15], [20,30]}  {[10,15], [18, 40]} = {[10,15]} Is such an operation useful \ commonsense \ meaningless for users?

ATELIC\TELIC ALGEBRA Ex.2TEMPORAL SELECTION (e.g., duration) All existing temporal algebrae are atelic. Indeed, most of them provide temporal selection (e.g., query about duration) But is duration something that can be evaluated “point-by-point” (snapshot-by-snapshot, i.e., in an atelic context) ? Indeed, duration regards the duration of minimal intervals covering convex sets of points! Thus, duration is about TIME INTERVALS, and thus regards the TELIC context.

ATELIC\TELIC ALGEBRA Indeed, a lot of confusion in the literature, since -The atelic view is chosen (nice properties!) - However, telic operators are useful, and thus “improperly” supported Part of the confusion is probably due to failing to recognize the distinction between syntax (representation) and semantics: Many approaches adopt intervals in the representation, probably not considering the fact that this does not mean supporting intervals in their semantics

ATELIC\TELIC ALGEBRA In a two-sorted domain with both atelic and telic relation, we need -A way of asking telic queries (e.g., queries about duration) on atelic data (and viceversa) -A way of querying both telic and atelic data in the same query NOTICE: the flexibility of moving from an atelic to a telic view of data, and viceversa, is provided in all natural languages! SOLUTION (Terenziani & Snodgrass, TKDE 2004): CONVERSION OPERATORS

ATELIC\TELIC ALGEBRA CONVERSION OPERATORS OPERATORS BETWEEN TIMEs: to-interval({1,2,3,4,7,8,9,11})  {[1,4],[7,9],[11,11]} to-point({[1,3],[4,4],[7,10]})  {1,2,3,4,7,8,9,10} NOTICE: to-interval(to-point({[1,3],[4,4],[7,10]}))  {[1,3],[4,4],[7,10]} There is a loss of information when moving from intervals to points!

ATELIC\TELIC ALGEBRA CONVERSION OPERATORS OPERATORS BETWEEN RELATIONSs: to-telic. Converts an atelic relation into a telic one, by leaving the non- temporal parts unchanged, and by applying the “to-interval” conversion to the temporal component of tuples to-atelic. Converts a telic relation into an atelic one, by leaving the non- temporal parts unchanged, and by applying the “to-point” conversion to the temporal component of tuples

ATELIC\TELIC ALGEBRA Examples Ex.1 “Who had a salary greater than 40K for more than 3 consecutive years, and what was her salary?” NameSalaryT Andrea60K{10,11,12} John50K{12,13} 10  { } 11  { } 12  {, } 13  { }  T duration  3 (to-telic(  A Salary>40 (EMP A )))

ATELIC\TELIC ALGEBRA Examples 10  { } 11  { } 12  {, } 13  { } r’=(  A Salary>40 (EMP A ) r”=(to-telic(r’)) [10,12]  { } [12,13]  { }  T duration  3 (r”) [10,12]  { }

ATELIC\TELIC ALGEBRA Examples Ex.2 “Who had a (complete) drug administration before the time when Andrea earned 50K?”  T Name (ADMIN T BEFORE (to-telic(  Name=Andrea, Salary=50K (EMP A )))

ATELIC\TELIC ALGEBRA Examples: Phone calls (PH) “Who made a (complete) phone call while John was calling Mary?” [10,12]  { } [12,14]  { } [13,15]  { } [14,16]  { } [15,16]  { } telic atelic telic  T Caller (PHONE T DURING (to-telic(to-atelic(  Caller=John, Called=Mary (PHONE T )))))

[10,12]  { } [12,14]  { } [13,15]  { } [14,16]  { } [15,16]  { } [10,12]  { } [12,14]  { } [13,15]  { } [14,16]  { } [15,16]  { } r=  Caller=John, Called=Mary (PH T ) PH T [10,12]  { } [13,15]  { } r’= to-atelic(r) r”= to-telic(r) 10  { } 11  { } 12  { } 13  { } 14  { } 15  { } [10,15]  { } DURING [10,12]  { } [12,14]  { } [13,15]  { }

Telic\Atelic extensions to SQL (e.g., TSQL2) Terenziani, Snodgrass et al., Artificial Intelligence in Medicine 39(2) , if no explicit indication is provided, temporal data are atelic. - definition of telic tables: “AS TELIC” clause in the TSQL2 CREATE TABLE statement. -by default, the result of queries is an atelic relation; - telic queries: prepend the keyword “TELIC” (i.e., “TELIC SELECT”). - Conversions functions

Implementation (Hint) -NOTICE 1: current temporal databases support the ATELIC view -NOTICE 2: current non-temporal databases (and current treatment of non-temporal data in temporal databases) support the TELIC view, in that neither upward nor downward inheritance are supported

Implementation (Hint) Starting from a temporal database, we have -The atelic treatment for free -The telic treatment by managing telic temporal tables as non-temporal ones - Conversions functions must be added

Conceptual Temporal Models Khatri, Ram, Snodgrass, Terenziani. IEEE TKDE. ISSN: Annotation-based temporal model 1)capturing “what” semantics using a conventional conceptual model; 2)annotations to differentiate between telic and atelic data semantics 3)(non-sequenced) temporal constraints as metadata

Conceptual Temporal Models Syntax of the annotations.  annotation  ::=є |  temporal annotation   temporal annotation  ::=є |  valid time  /  transaction time   valid time  ::=  state  (  g  ) |  event  (  g  ) | -  state  ::=  telic state  |  atelic state   transaction time  ::=T | Transaction | -  telic state  ::= Acc | Accomplishment  atelic state  ::= S | State | Atelic State  event  ::=E | Event

Conceptual Temporal Models Semantics of the annotations

Conceptual Temporal Models Semantics of the annotations Axiom 1: maximal_period and telic_period Telic periods (i.e., the valid times of VT_ACCOMPLISHMENTs) are well-formed.  e  S(VT_ACCOMPLISHMENT),  p  VT_ACCOMPLISHMENT(e, telic_period), begin(e, p) < end(e, p) Maximal temporal periods (i.e., the valid time of VT_STATEs) are well-formed.  e  S(VT_STATE),  p  VT_STATE(e, maximal_ period), begin(e, p) < end (e, p) Maximal temporal periods (i.e., the valid time of VT_STATEs) cannot overlap in time. Such a constraint does not hold for telic periods.  e  S(VT_STATE),  p 1, p 2  VT_STATE(e, maximal_ period), begin(e, p 1 ) < begin(e, p 2 )  end (e, p 1 ) < begin (e, p 2 )

Conceptual Temporal Models Semantics of the annotations Downward and upward inheritance (apply to VT_STATE) VT_Down  e, p 1, p 2, VT_STATE(e)  VT_STATE.hold(e, p 1 )  p 2  p 1  VT_STATE.hold(e, p 2 ) VT_Up  e, p 1, p 2, VT_STATE(e)  VT_STATE.hold(e, p 1 )  VT_STATE.hold(e, p 2 )  (MEETS(p 1, p 2 )  MEETS -1 (p 1, p 2 )  OVERLAPS(p 1, p 2 )  OVERLAPS -1 (p 1, p 2 )  FINISHED(p 1, p 2 )  FINISHED -1 (p 1, p 2 )  DURING(p 1, p 2 )  DURING -1 (p 1, p 2 )  STARTS(p 1, p 2 )  STARTS -1 (p 1, p 2 )  EQUALS(p 1, p 2 ) )  VT_STATE.hold(e, p 1  p 2 )

Conceptual Temporal Models Semantics of composition No Type of attribute/relationship (A/R) Type of entity class (EC) Coercion to atelic Semantics 1 є or non-temporal –Conventional 2 є or non-temporal S or VT_STATE –Infer A/R is temporal 3 є or non-temporal Acc or VT_ACCOMPLISHMENT ECInfer A/R is temporal 4 є or non-temporal E or VT_EVENT –Infer A/R is temporal 5 S or VT_STATE – 6 Acc or VT_ACCOMPLISHMENT EC 7 S or VT_STATEє or non-temporal –Infer EC is temporal 8 S or VT_STATEE or VT_EVENT – 9 Acc or VT_ACCOMPLISHMENT S or VT_STATE A/R 10 Acc or VT_ACCOMPLISHMENT EC, A/R 11 Acc or VT_ACCOMPLISHMENT є or non-temporal A/RInfer EC is temporal 12 Acc or VT_ACCOMPLISHMENT E or VT_EVENT A/R 13 E or VT_EVENTS or VT_STATE – 14 E or VT_EVENT Acc or VT_ACCOMPLISHMENT EC 15 E or VT_EVENTє or non-temporal –Infer EC is temporal 16 E or VT_EVENT – Interaction of temporal/non-temporal attribute/relationship with temporal/non-temporal entity class

Conclusions The telic\atelic dichotomy seems to be an intrinsic part of human way of dealing with reality (speaking, modeling, …) Not coping with such a dichotomy leads to modeling errors in temporal databases New approach to cope with the telic\atelic dichotomy -In the data model -In the relational algebra -In a SQL-like query language -In conceptual modeling Future work (open challenges): - aggregation - data warehousing - spatial data