Towards truth in HPSG

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Towards truth in HPSG

• Paul John King

2
Intention

• Characterisation of truth in HPSG

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Content

• Section 1 Linguistic tokens as suitable media or
  characterisation of truth in HPSG
• Section 2 Outlines a particular construal of a
  HPSG linguistic token based largely upon the
  structure of HPSG 94 sort hierarchy imposes upon
  such a token
• Section 3 SRL signature instead of HPSG 94 sort
  hierarchy
• Section 4 Characterisation of truth

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1. Introduction

• Relationship between a grammar and a NL according
  to HPSG 94
• 1. Partition of the universe of ontological
  categories of the empirical domain (sorts of
  constructs)
• 2. Mathematical structures used t model them.
• Thus-gt formalisation

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Truth of a grammar (HPSG 94)

• Modelling domain system of FSs that stand in
  one-to-one relation with types of NL expressions
  and their subparts
• Predictions of the theory types of linguistic
  entities that correspond to the admissible
  feature structures
• A grammar of a NL predicts a linguistic type iff
  the grammar admits the FS that corresponds to the
  linguistic type
• A grammar of a NL is true only if the grammar
  predicts all and only the linguistic types in the
  NL

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What is language

• The linguistic knowledge shared by the community
  of speakers of a specific language
• Consists of
• A .System of linguist. Types
• V
• B. Individual linguistic events (utterance
  tokens)
• Types are assumed to be classes of linguistic
  tokens

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Questioning the linguistic types

• Psycholinguistic evidence
• Tokens are empirical
• But types are not (example page 307)

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Objections to HPSG 94 characterisation of truth

• Much of the formal machinery is superfluous
• HPSG 94 characterisation is poorly defined (The
  nature of FSs is not clearly defined. Are they
  concrete or abstract?)
• HPSG 94 is ambiguous, silent or contradictory
  about ist formal machinery (e.g. does not account
  for infinite linguistic types p.314)
• Intuitive baggage of total well-typedness and
  sort-resolvedness of FSs that a grammarian is
  hard to bear.

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2. Ontology

• What is a linguistic token?
• Actual and nonactual tokens
• Token-based truth characterisation
• A grammar of a NL is true if it comprises only
  those tokens of the mature users of a NL
• Theoretical claims about linguistic knowledge
  should be based only on experimental testing of
  consequent claims about linguistic behaviour.

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Resolution of ambiguity in sort hierarchy of HPSG
94

• Page 318,319
• For 2 sorts s and t, t is a subsort of s iff it
  is dominated by s.

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3. Formalism

• Inefficiency of Kasper and Rounds logic
• Need for a formal language

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Basic terms (p. 322)

• Signature Provides the nonlogical symbols from
  which the descriptions are constr.
• Interpretation
• Provides the Univ. of entities
• Assigns each nonlogical symbol in the S a meaning
• I is trivial when U is empty
• Description Finite well-formed string of logical
  symbols and symbols from the S
• Appropriateness function

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Basic definitions

• U is partitioned by sets of entities denoted by
  each species u e U such that S(u)s
• S assigns each entity the unique species that
  denotes the set it belongs to.
• F assigns each feature the partial function it
  denotes
• A encodes a strict relationship between the
  denotations of features and species (page 323)
• Terms, descriptions and theories (p 323)

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Truth of descriptions and theories (p.324)

• I satisfies (on board)
• I models
• In SRL an interpretation may satisfy a theory yet
  not model it or may model a theory yet not
  satisfy it.
• Extended example page 325

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HPSG in SRL

• HPSG Sort hierarchy and set of principles
• A sort hierarchy can be expressed as a S (p. 329)
• Information encoded in a sort hierarchy
  denotations of sorts and features
• This information can be easily inferred from the
  corresponding S. (p. 329-330)
• A set of principles can be expressed as a theory
  (examples p. 331).

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HPSG principles in SRL

• 1. Addition of relations and functions (concat,
  extract) -gt RSRL
• 2.JUNK slots (ad hoc, cumbersome,
  counterintuitive)

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Expression-emulation of HPSG grammar through SRL

• SRL can express many aspects of HPSG which are
  loosely formulated
• 1. S vs inheritance
• 2. Notion of lex. Rules
• 3. Phonology
• 4. Word order

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Summary

• A HPSG grammar can be expressed in very large
  part, if not entirety, as a SRL grammar, where a
  SRL grammar is a pair (S,?) such that S is a
  signature and ? is a subset of DS

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TruthInterim Thesis 1

• A grammar is true of a natural language only if
  the natural language can be construed as a system
  of linguistic tokens meeting the conditions
  imposed upon them by the S of the grammar.
• For each Grammar G(S,?), for each natural
  language I,
• If G is true of I
• Then I is an interpretation of S

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Interim Thesis 2

• A grammar is true of a natural language only if
  each description in the theory component of the
  grammar is true of each entity in the natural
  language.
• For each Grammar G(S,?), for each natural
  language I,
• If G is true of I
• Then I is an interpretation of S, and
• I models ? in S.

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Interim Thesis 3

• A grammar is true of a natural language only if
  the theory component of the grammar is false of
  each entity not in the natural language.
• For each Grammar G(S,?), for each natural
  language I,
• If G is true of I
• Then I is an interpretation of S,
• I models ? in S, and
• for each interpretation I of S, for each u ?
  I,
• if u ? TI(?) then u ? I.

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Interim Thesis 4

• A grammar is true of a natural language only if
  the theory component of the grammar is false of
  some constituent of each entity not in the
  natural language.
• Formalisation -gt p. 339

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Interim Thesis 5

• A grammar is true of a natural language only if
  the theory component of the grammar is false of
  some constituent of each entity with a
  constituent configuration not in the NL.
• P. 341

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Interim Thesis 6

• A grammar is true of a natural language only if
  the theory component of the grammar is false of
  some constituent of each linguistic entity with a
  constituent configuration not in the NL.
• P.341,342

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Thesis 1

• A grammar (S,?) is true of a NL only if
• The natural language can be construed as a system
  of linguistic tokens meeting the conditions
  imposed on them by S,
• Each d in ? is true of each entity in the NL and,
• Some d in ? is false of some constituent of each
  entity for which no entity in the NL has
  isomorphically configured constituents.
• P. 343

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Propositions 1 and 2

• Better formulations of Thesis 1
• P. 343, 344

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Thesis 2

• For each Grammar G(S,?), for each natural
  language I,
• If G is true of I
• Then I is an interpretation of S and
• I exhaustively models ? in S

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Theorem 1

• For each Grammar G(S,?), for some interpretation
  I of S, I exhaustively models ? ?n S