Timelines from Text Finding Event Order and Relations in Narratives - PowerPoint PPT Presentation

Stuttering Strings Since we don’t assign a fixed duration to any Being able to intentionally introduce and remove box, the strings may stutter without its stutter in a string will be convenient in the next interpretation being affected. section. A string component can stutter any number of times in this way. ≡ a a, b b a a, b a, b b

Stuttering Strings Since we don’t assign a fixed duration to any Being able to intentionally introduce and remove box, the strings may stutter without its stutter in a string will be convenient in the next interpretation being affected. section. A string component can stutter any number of We will consider a string with no stutter to be times in this way. the simplest representation of that sequence of events. ≡ a a, b b a a, b a, b b

An Assumption One assumption to take note of here is that each symbol in our fluent alphabet names an event instance , rather than an event.

An Assumption One assumption to take note of here is that each symbol in our fluent alphabet names an event instance , rather than an event. This means that if an event were to stop, and then start again later, the distinct parts must be named uniquely.

An Assumption One assumption to take note of here is that each symbol in our fluent alphabet names an event instance , rather than an event. This means that if an event were to stop, and then start again later, the distinct parts must be named uniquely. This prevents confusion and helps identify inconsistencies.

An Assumption One assumption to take note of here is that each For example, “It rained from 10 till noon, then symbol in our fluent alphabet names an event again from 3 till 9.” instance , rather than an event. This means that if an event were to stop, and then start again later, the distinct parts must be named uniquely. This prevents confusion and helps identify inconsistencies.

An Assumption One assumption to take note of here is that each For example, “It rained from 10 till noon, then symbol in our fluent alphabet names an event again from 3 till 9.” instance , rather than an event. Rather than looking like This means that if an event were to stop, and rain rain then start again later, the distinct parts must be named uniquely. This prevents confusion and helps identify inconsistencies.

An Assumption One assumption to take note of here is that each For example, “It rained from 10 till noon, then symbol in our fluent alphabet names an event again from 3 till 9.” instance , rather than an event. Rather than looking like This means that if an event were to stop, and rain rain then start again later, the distinct parts must be named uniquely. A well-formed string will be more like This prevents confusion and helps identify rain 1 rain 2 inconsistencies.

A well-formed string will look like rain 1 rain 2 A realistic, Irish string will look like... rain rain rain

Combinations of Worlds

Strings As Worlds In essence, each string is a small representation of a world, one denoted by the events we are interested in.

Strings As Worlds In essence, each string is a small representation of a world, one denoted by the events we are a b c interested in. A world where a happened, then b , then c .

Strings As Worlds In essence, each string is a small representation of a world, one denoted by the events we are a b c interested in. A world where a happened, then b , then c . Different strings may represent different worlds, describing alternate sequences of events which took place.

Strings As Worlds In essence, each string is a small representation of a world, one denoted by the events we are a b c interested in. A world where a happened, then b , then c . Different strings may represent different worlds, describing alternate sequences of events which c d a took place. A world where c happened before a , and d happened between them instead of b .

Strings As Worlds In essence, each string is a small representation of a world, one denoted by the events we are a b c interested in. A world where a happened, then b , then c . Different strings may represent different worlds, describing alternate sequences of events which c d a took place. Separate strings might also represent different A world where c happened before a , and d projections of the same world. happened between them instead of b .

Projections Some terminology:

Projections Some terminology: ● Vocabulary of a string: the set of fluents appearing in that string

Projections Some terminology: ● Vocabulary of a string: the set of fluents appearing in that string ● Reduct (wrt some set A ): an operation to reduce the vocabulary of a string to just the fluents appearing in A

Projections Some terminology: ● Vocabulary of a string: the set of fluents appearing in that string ● Reduct (wrt some set A ): an operation to reduce the vocabulary of a string to just the fluents appearing in A We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = s'

Projections Some terminology: ● Vocabulary of a string: the set of fluents appearing in that string ● Reduct (wrt some set A ): an operation to reduce the vocabulary of a string to just the fluents appearing in A We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = s'

Projections Some terminology: ● Vocabulary of a string: the set of fluents appearing in that string ● Reduct (wrt some set A ): an operation to reduce the vocabulary of a string to just the fluents appearing in A We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = s' i.e. Reducing s to the vocabulary of s' and then removing any stutter produces s' .

Projections Some terminology: For example: ● Vocabulary of a string: the set of fluents appearing in s = a b, c c, d d s' = a d that string ● Reduct (wrt some set A ): an operation to reduce the vocabulary of a string to just the fluents appearing in A We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = s' i.e. Reducing s to the vocabulary of s' and then removing any stutter produces s' .

Projections Some terminology: For example: ● Vocabulary of a string: the set of fluents appearing in s = a b, c c, d d s' = a d that string ● Reduct (wrt some set A ): an operation to reduce the voc(s') = {a, d} vocabulary of a string to just the fluents appearing in A We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = s' i.e. Reducing s to the vocabulary of s' and then removing any stutter produces s' .

Projections Some terminology: For example: ● Vocabulary of a string: the set of fluents appearing in s = a b, c c, d d s' = a d that string ● Reduct (wrt some set A ): an operation to reduce the voc(s') = {a, d} vocabulary of a string to just the fluents appearing in A ρ voc(s') (s) = a d d We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = s' i.e. Reducing s to the vocabulary of s' and then removing any stutter produces s' .

Projections Some terminology: For example: ● Vocabulary of a string: the set of fluents appearing in s = a b, c c, d d s' = a d that string ● Reduct (wrt some set A ): an operation to reduce the voc(s') = {a, d} vocabulary of a string to just the fluents appearing in A ρ voc(s') (s) = a d d We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = a d = s' bc( ρ voc(s') (s)) = s' i.e. Reducing s to the vocabulary of s' and then removing any stutter produces s' .

Projections Some terminology: For example: ● Vocabulary of a string: the set of fluents appearing in s = a b, c c, d d s' = a d that string ● Reduct (wrt some set A ): an operation to reduce the voc(s') = {a, d} vocabulary of a string to just the fluents appearing in A ρ voc(s') (s) = a d d We say a string s projects to another s' iff: bc( ρ voc(s') (s)) = a d = s' bc( ρ voc(s') (s)) = s' ∴ s projects to s' i.e. Reducing s to the vocabulary of s' and then removing any stutter produces s' .

Superposition of Strings Strings become more useful when we can combine them together - fusing multiple views of a world into a single sequence.

Superposition of Strings Strings become more useful when we can combine them together - fusing multiple views of a world into a single sequence. For example, if we have two strings a b and b c , then it would be convenient to collapse these into a single string: a b c .

Superposition of Strings Strings become more useful when we can combine them together - fusing multiple views of a world into a single sequence. For example, if we have two strings a b and b c , then it would be convenient to collapse these into a single string: a b c . Not only is this more compact, it allows us to determine that a occurred before c - not obvious from either original string alone.

Superposition of Strings Strings become more useful when we can We can do this using superposition . combine them together - fusing multiple views of a world into a single sequence. For example, if we have two strings a b and b c , then it would be convenient to collapse these into a single string: a b c . Not only is this more compact, it allows us to determine that a occurred before c - not obvious from either original string alone.

Superposition of Strings Strings become more useful when we can We can do this using superposition . combine them together - fusing multiple views In its most basic form, this is just the of a world into a single sequence. component-wise union of two strings: For example, if we have two strings a b and x y & p q = x, p y, q b c , then it would be convenient to collapse these into a single string: a b c . Not only is this more compact, it allows us to determine that a occurred before c - not obvious from either original string alone.

Superposition of Strings Strings become more useful when we can We can do this using superposition . combine them together - fusing multiple views In its most basic form, this is just the of a world into a single sequence. component-wise union of two strings: For example, if we have two strings a b and x y & p q = x, p y, q b c , then it would be convenient to collapse these into a single string: a b c . Following a more complex algorithm allows superposition to asynchronously combine Not only is this more compact, it allows us to strings of differing lengths which are projections determine that a occurred before c - not obvious of the same world. from either original string alone.

Superposition of Strings 1. Introduce stutter into one or both of the strings to be superposed.

Superposition of Strings 1. Introduce stutter into one or both of the strings to be superposed. 2. Select strings of equal length, and perform basic superposition.

Superposition of Strings 1. Introduce stutter into one or both of the strings to be superposed. 2. Select strings of equal length, and perform basic superposition. 3. Reject results which will not be well-formed (i.e. break our assumption of non-resumptive events) - we can also impose other external constraints here.

Superposition of Strings 1. Introduce stutter into one or both of the strings to be superposed. 2. Select strings of equal length, and perform basic superposition. 3. Reject results which will not be well-formed (i.e. break our assumption of non-resumptive events) - we can also impose other external constraints here. 4. Collect set of remaining results.

Superposition of Strings 1. Introduce stutter into one or both of the strings to be superposed. 2. Select strings of equal length, and perform basic superposition. 3. Reject results which will not be well-formed (i.e. break our assumption of non-resumptive events) - we can also impose other external constraints here. 4. Collect set of remaining results. Full details of the algorithm can be found here: https://www.scss.tcd.ie/~dwoods/isa14

Languages As Parallel Worlds Superposing in this asynchronous way can result in a set of strings (called a language ) as output.

Languages As Parallel Worlds Superposing in this asynchronous way can result in a set of strings (called a language ) as output. This occurs when there is some unresolved ambiguity.

Languages As Parallel Worlds Superposing in this asynchronous way can result in a set of strings (called a language ) as output. This occurs when there is some unresolved ambiguity. e.g. a b & a c = ?

Languages As Parallel Worlds Superposing in this asynchronous way can result in a set of strings (called a language ) as output. This occurs when there is some unresolved ambiguity. e.g. a b & a c = ? We don’t know the relation between b and c in this scenario. Superposition will generate a string for every possibility.

Languages As Parallel Worlds Superposing in this asynchronous way can The strings in a language are alternate timelines result in a set of strings (called a language ) as of a single world. Each is equally possible if we output. don’t have more information. This occurs when there is some unresolved ambiguity. e.g. a b & a c = ? We don’t know the relation between b and c in this scenario. Superposition will generate a string for every possibility.

Languages As Parallel Worlds Superposing in this asynchronous way can The strings in a language are alternate timelines result in a set of strings (called a language ) as of a single world. Each is equally possible if we output. don’t have more information. This occurs when there is some unresolved Languages may also be superposed - this can ambiguity. either increase or decrease the number of possible timelines depending on what e.g. a b & a c = ? information is introduced. We don’t know the relation between b and c in this scenario. Superposition will generate a string for every possibility.

Languages As Parallel Worlds Superposing in this asynchronous way can The strings in a language are alternate timelines result in a set of strings (called a language ) as of a single world. Each is equally possible if we output. don’t have more information. This occurs when there is some unresolved Languages may also be superposed - this can ambiguity. either increase or decrease the number of possible timelines depending on what e.g. a b & a c = ? information is introduced. We don’t know the relation between b and c in In some cases it may also be possible to change this scenario. Superposition will generate a the nature of our basic units to conflate a string for every possibility. language with a single string...

Try to avoid having too many parallel worlds!

Intervals, Points, and Borders

Basic Units The type of unit we treat as basic can have a significant impact on the complexity and accuracy of the strings.

Basic Units The type of unit we treat as basic can have a significant impact on the complexity and accuracy of the strings. Three main options to consider: intervals, points, and semi-intervals.

Basic Units The type of unit we treat as basic can have a significant impact on the complexity and accuracy of the strings. Three main options to consider: intervals, points, and semi-intervals. There is a translation to compress intervals to points, but the inverse is not possible. We can also translate intervals to semi-intervals, and the inverse is often (but not necessarily) possible.

Allen’s Interval Algebra Intervals have some duration.

Allen’s Interval Algebra Intervals have some duration. They can overlap, and so can be arranged in more ways than points can.

Allen’s Interval Algebra Intervals have some duration. They can overlap, and so can be arranged in more ways than points can. The thirteen possibilities for a pair of intervals are known as Allen Relations, after James Allen’s 1983 work.

Allen’s Interval Algebra Intervals have some duration. They can overlap, and so can be arranged in more ways than points can. The thirteen possibilities for a pair of intervals are known as Allen Relations, after James Allen’s 1983 work. Can be subdivided into smaller intervals if desired.

Allen’s Interval Algebra Intervals have some duration. Used in annotation systems such as TimeML: They can overlap, and so can be arranged in <TLINK relType=" IS_INCLUDED " timeID="t1" relatedToEventInstance="ei9"/> more ways than points can. The thirteen possibilities for a pair of intervals are known as Allen Relations, after James Allen’s 1983 work. Can be subdivided into smaller intervals if desired.

Allen’s Interval Algebra Intervals have some duration. Used in annotation systems such as TimeML: They can overlap, and so can be arranged in <TLINK relType=" IS_INCLUDED " timeID="t1" relatedToEventInstance="ei9"/> more ways than points can. Interestingly, the thirteen relations fall out of The thirteen possibilities for a pair of intervals superposing two strings that each feature a are known as Allen Relations, after James single interval. Allen’s 1983 work. Can be subdivided into smaller intervals if desired.

Allen’s Interval Algebra a b b a a b b a a b a, b b a, b a a b b b a, b a a, b a & = a, b b a, b a b a, b a a, b a, b

Allen’s Interval Algebra a b b a a b b a a b a, b b a, b a a b b b a, b a a, b a & = a, b b a, b a Border boxes show that b a, b a a, b the interval is finite a, b

Point-based Strings Durationless points are an alternative to intervals.

Point-based Strings Durationless points are an alternative to intervals. A pair of points can only be arranged in three ways: before, equals, after.

Point-based Strings Durationless points are an alternative to intervals. A pair of points can only be arranged in three ways: before, equals, after. Fewer possible arrangements means fewer outcomes from combining strings.

Point-based Strings Durationless points are an alternative to intervals. A pair of points can only be arranged in three ways: before, equals, after. Fewer possible arrangements means fewer outcomes from combining strings. Lower complexity, but at the cost of accuracy…

Point-based Strings Durationless points are an alternative to intervals. A pair of points can only be arranged in three ways: before, equals, after. Fewer possible arrangements means fewer outcomes from combining strings. Lower complexity, but at the cost of accuracy… For example, “During breakfast, I ate cereal, then ate toast.”