Combinatorial Semantics
The challenge of combinatorial semantics is to
be able to assign exactly one semantic representation
to each word and sub-phrase regardless
of its surrounding context, and to combine
these representations in a systematic way until
the representation for the entire sentence is obtained.
There are many linguistic constructions
in the puzzles whose compositional analysis is
difficult, such as a large variety of noun-phrase
structures (e.g., “Every sculpture must be exhibited
in a different room”) and ellipses (e.g.,
“Brian saw a taller man than Carl [did]”).
Scope Ambiguities
A sentence has a scope ambiguity when quantifiers
and other operators in the sentence can
have more than one relative scope. E.g., in constraint
(4) of Figure 1, “each room” outscopes
“at least one sculpture”, but in other contexts,
the reverse scoping is possible. The challenge
is to find, out of all the possible scopings, the
appropriate one, to understand the text as the
writer intended.
Reference Resolution
The puzzle texts contain a wide variety of
anaphoric expressions, including pronouns, definite
descriptions, and anaphoric adjectives. The
challenge is to identify the possible antecedents
that these expressions refer to, and to select
the correct ones. The problem is complicated
by the fact that anaphoric expressions interact
with quantifiers and may not refer to any particular
context element. E.g., the anaphoric expressions
in “Sculptures C and E are exhibited
in the same room” and in “Each man saw a different
woman” interact with sets ({C,E} and
the set of all men, respectively).
Plurality Disambiguation
Sentences that include plural entities are potentially
ambiguous between different readings:
distributive, collective, cumulative, and combinations
of these. For example, sentence 1 in
Figure 1 says (among other things) that each
of the six sculptures is displayed in one of the
three rooms – the group of sculptures and the
group of rooms behave differently here. Plurality
is a thorny topic which interacts in complex
ways with other semantic issues, including
quantification and reference.
Lexical Semantics
The meaning of open-category words is often
irrelevant to solving a puzzle. For example,
the meaning of “exhibited”, “sculpture”, and
“room” can be ignored because it is enough to
understand that the first is a binary relation
that holds between elements of groups described
by the second and third words.1 This observa-
tion provides the potential for a general system
that solves logic puzzles.
Of course, in many cases, the particular
meaning of open-category words and other expressions
is crucial to the solution. An example
is provided in question 2 of Figure 1: the system
has to understand what “a complete list”
means. Therefore, to finalize the meaning computed
for a sentence, such expressions should be
expanded to their explicit meaning. Although
there are many such cases and their analysis is
difficult, we anticipate that it will be possible to
develop a relatively compact library of critical
puzzle text expressions. We may also be able
to use existing resources such as WordNet and
FrameNet.
Information Gaps
Natural language texts invariably assume some
knowledge implicitly. E.g., Figure 1 does not explicitly
specify that a sculpture may not be exhibited
in more than one room at the same time.
Humans know this implicit information, but a
computer reasoning from texts must be given
it explicitly. Filling these information gaps is
a serious challenge; representation and acquisition
of the necessary background knowledge are
very hard AI problems. Fortunately, the puzzles
domain allows us to tackle this issue, as
explained in §8.
Presuppositions and Implicatures
In addition to its semantic meaning, a natural
language text conveys two other kinds of content.
Presuppositions are pieces of information assumed
in a sentence. Anaphoric expressions
bear presuppositions about the existence of entities
in the context; the answer choice “Sculptures
C and E” conveys the meaning {C,E},
but has the presupposition sculpture(C) ^
sculpture(E); and a question of the form A !
B, such as question 1 in Figure 1, presupposes
that A is consistent with the preamble.
Implicatures are pieces of information suggested
by the very fact of saying, or not saying,
something. Two maxims of (Grice, 1989)
dictate that each sentence should be both consistent
and informative (i.e. not entailed) with
respect to its predecessors. Another maxim dictates
saying as much as required, and hence the
sentence “No more than three sculptures may be
exhibited in any room” carries the implicature
that in some possible solution, three sculptures
are indeed exhibited in the same room.
Systematic calculation of presuppositions and
implicatures has been given less attention in
NLP and is less understood than the calculation
of meaning. Yet computing and verifying
them can provide valuable hints to the system
whether it understood the meaning of the text
correctly.
The challenge of combinatorial semantics is to
be able to assign exactly one semantic representation
to each word and sub-phrase regardless
of its surrounding context, and to combine
these representations in a systematic way until
the representation for the entire sentence is obtained.
There are many linguistic constructions
in the puzzles whose compositional analysis is
difficult, such as a large variety of noun-phrase
structures (e.g., “Every sculpture must be exhibited
in a different room”) and ellipses (e.g.,
“Brian saw a taller man than Carl [did]”).
Scope Ambiguities
A sentence has a scope ambiguity when quantifiers
and other operators in the sentence can
have more than one relative scope. E.g., in constraint
(4) of Figure 1, “each room” outscopes
“at least one sculpture”, but in other contexts,
the reverse scoping is possible. The challenge
is to find, out of all the possible scopings, the
appropriate one, to understand the text as the
writer intended.
Reference Resolution
The puzzle texts contain a wide variety of
anaphoric expressions, including pronouns, definite
descriptions, and anaphoric adjectives. The
challenge is to identify the possible antecedents
that these expressions refer to, and to select
the correct ones. The problem is complicated
by the fact that anaphoric expressions interact
with quantifiers and may not refer to any particular
context element. E.g., the anaphoric expressions
in “Sculptures C and E are exhibited
in the same room” and in “Each man saw a different
woman” interact with sets ({C,E} and
the set of all men, respectively).
Plurality Disambiguation
Sentences that include plural entities are potentially
ambiguous between different readings:
distributive, collective, cumulative, and combinations
of these. For example, sentence 1 in
Figure 1 says (among other things) that each
of the six sculptures is displayed in one of the
three rooms – the group of sculptures and the
group of rooms behave differently here. Plurality
is a thorny topic which interacts in complex
ways with other semantic issues, including
quantification and reference.
Lexical Semantics
The meaning of open-category words is often
irrelevant to solving a puzzle. For example,
the meaning of “exhibited”, “sculpture”, and
“room” can be ignored because it is enough to
understand that the first is a binary relation
that holds between elements of groups described
by the second and third words.1 This observa-
tion provides the potential for a general system
that solves logic puzzles.
Of course, in many cases, the particular
meaning of open-category words and other expressions
is crucial to the solution. An example
is provided in question 2 of Figure 1: the system
has to understand what “a complete list”
means. Therefore, to finalize the meaning computed
for a sentence, such expressions should be
expanded to their explicit meaning. Although
there are many such cases and their analysis is
difficult, we anticipate that it will be possible to
develop a relatively compact library of critical
puzzle text expressions. We may also be able
to use existing resources such as WordNet and
FrameNet.
Information Gaps
Natural language texts invariably assume some
knowledge implicitly. E.g., Figure 1 does not explicitly
specify that a sculpture may not be exhibited
in more than one room at the same time.
Humans know this implicit information, but a
computer reasoning from texts must be given
it explicitly. Filling these information gaps is
a serious challenge; representation and acquisition
of the necessary background knowledge are
very hard AI problems. Fortunately, the puzzles
domain allows us to tackle this issue, as
explained in §8.
Presuppositions and Implicatures
In addition to its semantic meaning, a natural
language text conveys two other kinds of content.
Presuppositions are pieces of information assumed
in a sentence. Anaphoric expressions
bear presuppositions about the existence of entities
in the context; the answer choice “Sculptures
C and E” conveys the meaning {C,E},
but has the presupposition sculpture(C) ^
sculpture(E); and a question of the form A !
B, such as question 1 in Figure 1, presupposes
that A is consistent with the preamble.
Implicatures are pieces of information suggested
by the very fact of saying, or not saying,
something. Two maxims of (Grice, 1989)
dictate that each sentence should be both consistent
and informative (i.e. not entailed) with
respect to its predecessors. Another maxim dictates
saying as much as required, and hence the
sentence “No more than three sculptures may be
exhibited in any room” carries the implicature
that in some possible solution, three sculptures
are indeed exhibited in the same room.
Systematic calculation of presuppositions and
implicatures has been given less attention in
NLP and is less understood than the calculation
of meaning. Yet computing and verifying
them can provide valuable hints to the system
whether it understood the meaning of the text
correctly.
No comments:
Post a Comment