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Formalization and Implementation of Cognitive Semantics

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Title: Formalization and Implementation of Cognitive Semantics


1
Formalization and Implementation of Cognitive
Semantics
Joseph A Goguen
Computer Science Engineering
University of California at San
Diego Thanks to Fox Harrell for help with
slides research.
2
1. Introduction
  • How to design human friendly ontologies?
  • Mathematics, physics, formal philosophy are not
    always friendly!
  • - top down often counter-intuitive.
  • - also culture specific
  • - Barry Smith, John Sowa, Robert Kent
  • Most real ontologies built bottom up -
    B2B, ecology (EML), etc.

3
1. Introduction
  • Why not use cognitively real constructs? -
    basic level concepts
  • - basic image schemas
  • - combine with blending, etc.
  • - especially good for spatial ontologies.
  • Evidence favors middle-out as human
  • - See work of Rosch below.

4
2. Goals Methods of Cognitive Semantics
  • Goals
  • - Understand language/mind/body interface
  • - Understand concepts meaning
  • - Understand how mind works
  • Methods
  • - Careful analysis of large bodies of language
  • (spoken, written, graphics)
  • - Introspection (members competance)

5
3. Rosch Experiments on Human Concepts
  • In is_a hierarchy, basic level is in middle,
    has shortest name, most rapid identification,
    most associated knowledge, earliest learned
  • - since has most human interaction
  • Highest level such that prototype exists, image
    representing whole category similar motor
    actions for interaction with all instances.

6
3. Human Concepts
  • Examples
  • - shoe, not footwear, or sneakers
  • - apple, not fruit, or Macintosh
  • - PC, not machine, or Macintosh
  • Basic level concepts have maximal amount of
    internal structure
  • - Could vary with user community

7
4. Conceptual Spaces, Frames Domains
  • Fauconnier mental spaces are first order
    relational structures (mostly binary)
  • But theories are better declarations axioms
  • Frame is densely interconnected system of
    concepts
  • - Family father, mother, son, daughter,
  • - Chair with legs, seat, back,
  • Domain is larger collection of more loosely
    connected concepts (e.g., law, education)

8
5. Lakoff Metaphor Theory
  • Image Schemas embodied gestalt
  • - Container
  • - Journey
  • - In/Out (is blend of two above)
  • Examples
  • - He is trapped in his confusion.
  • - I dont know where Im going anymore.
  • - She cant get out of her old habits.

9
5. Lakoff Metaphor Theory
  • Metaphor is conceptual space map
  • - map is asymmetric
  • concrete source to abstract target
  • - map is partial not all source used
  • - understand target via source
  • - both entities inferences mapped

10
Examples
  • Metaphor
  • - The sun is a king
  • - Theories are constructed objects
  • Metonymy one thing stands for another e.g.,
    part for whole
  • - Paris disapproves of our Iraq policy
  • - Is not map, but internal to one space

11
An Extended Example
  • Theories are constructed objects
  • - Major premises are foundations
  • - Major claims arguments are structure
  • - Facts are material constituents
  • - Arguments are mortar of facts claims
  • - Logical strength is design or architecture
  • - Theorist is architect
  • - Believability is strength
  • - Persistence is successful standing
  • - Failure is collapse

12
6. Fauconnier TurnerConceptual Blending
  • Conceptual Space Networks
  • Simple blend diagram input spaces generic
    space

13
Conceptual Blending
  • Some strong claims for blending
  • - is foundation of human thought
  • - including reasoning perception
  • - is unconscious rapid
  • But are many choices for blending
  • - so optimality principles are needed
  • to decide among them.

14
Houseboat Example
15
Boathouse Blend Space
16
More Examples
  • 48 major blends for house boat!
  • Oxymorons
  • - Military intelligence
  • - New classic
  • - Microsoft works
  • Counterfactuals
  • - In South Africa, Watergate wouldnt
  • have done Nixon any harm.
  • - If I were you, Id do nit now.

17
7. Fauconnier TurnerMetaphor Theory
  • Use blending not mapping
  • Cross space map emergent from whats in blend
    space
  • New emergent structure (see below)
  • Main optimality principle Relations compressed
    to human scale

18
Example Climbing Monks
19
8. Common Sense Optimality Principles
  • All are very informal
  • Well-integrated scene
  • Web tight Connections between blend inputs
    (e.g. event in one input space construed to imply
    event in blend)
  • Unpacking easy to recover inputs connections
    from blend
  • Topology elements in blend should be in same
    kinds of relation as counterparts in inputs
  • Good Reasoning elements in blend should have
    meaning
  • Integration scenario in blend space should have
    meaning
  • Metonymic Tightening relations of elements from
    same input should become as close as possible in
    blend.

20
Formal Optimality Principles
  • Type preservation
  • Arity (number of arguments)
  • Axiom preservation
  • Level priority preservation
  • These can be checked by computer
  • They are implementable.

21
9. Promise Problems
  • New Developments
  • - Experimental studies of gesture
  • - Computer models of spatial
  • prepositions, verb, modes, image
  • schemas, using Petri nets
  • Dynamic, exciting field, relevant to many other
    fields

22
  • Problems with Conceptual Spaces
  • - Space cannot change over time
  • - No constructors for structure
  • - Fixed common sense optimality
  • principles
  • - But need disoptimality multi-
  • grain optimality principles (see below)

23
Examples for New Principles
  • Many modern poets go against what readers (used
    to) expect, e.g., Neruda
  • I am withered, impervious, like a swan of
    felt
  • navigating a water of beginning and ashes.
  • Or Rilke
  • cheap winter hats of fate
  • For this, need disoptimality principles
  • Also structure at multiple granularities

24
10. Extensions
  • Conceptual blending good for language, but needs
    extending for other media
  • Such as
  • - Computational narrative
  • - User-interface design
  • - Gaming
  • - Database Integration, Querying

25
Three Levels of Languge
  • Discourse
  • Sentence
  • Phrase (Including metaphor)
  • Treated differently in our generative system for
    pragmatic purposes, but are not really distinct

26
11. Labov Narrative Structure
  • Structure of narratives of personal experience,
    work of William Labov Charlotte Linde
  • - Optional orientation section gives time,
    place, characters, etc.
  • - Narrative clauses describe events, by default,
    occur in same order as in story
  • - Narrative clauses interwoven with evaluative
    material, are interpretative or evaluative
    information
  • - Optional closing section summarizes story or
    gives moral.

27
  • Labov Structure in Extended BNF
  • ltNarrgt ltOpengt (ltClsgt ltEvalgt) ltCodagt
  • ltOpengt ((ltAbsgt ltOrntgt) ltEvalgt)
  • We can also use other narrative structure
  • grammars for top level of generation systems,
  • e.g., postmodern, jumpcut, flashback,

28
12. Algebraic Semiotics
  • Semiotic spaces consist of sorts, relations,
    axioms constants, with partial order on each,
    primary sort
  • Semiotic morphisms are partial maps between
    semiotic spaces
  • Algebraic semiotics is brand name not aligned
    with contemporary semiotics, though influenced by
    Peirce Saussure

29
  • Builds on algebraic semantics abstract data
    type theory
  • Users insights from cognitive linguistics
    conceptual blending
  • Nice math definition of blending
  • lax colimit in enriched category (3/2 colimit
    in 3/2 category)
  • Assumes ordering on morphisms
  • as way to determine best blends

30
Data Structure for Conceptual Blending
31
13. Structural Blending
  • Generative media need structure, not just
    concepts about structure (e.g., for syntax
    discourse)
  • Templates act as constructors (which are
    functions)
  • Blending is textual substition then
  • cleaning up but we can do better
  • in the future

32
Active Poetry System
33
The Girl with Skin of Haints and Seraphs
  • her tale began when she was infected with
    scaled-being first-borntis
  • female oppressed vapor steamed from her pores
    when she rode her bicycle
  • death was better
  • she fears only female spectres
  • she loves only black ghosts
  • they inspire her
  • when she was no longer a child, Exu skin marks
    streaked her thighs
  • her lips danced with love and pride.
  • it was no laughing matter
  • love and pride no longer concerned her when she
    was elderly
  • her charcoal-girl soul life saddened her
  • so she no longer flies with evil shame
  • she only sings out that evil pride devours and
    alternates-with hope pride.

34
  • ((her tale began when she was infected with
    (scaled-being / first-born) -itis)
  • ((female / oppressed) vapor steamed from her
    pores when she rode her bicycle)
  • (death was better) (she fears only (female /
    spectre)) (she loves only (black / ghost))
  • (it inspired her) (when she was no longer a child
    (exu / skin) marks streaked her thighs)
  • (her lips danced with (love / pride)) (it was no
    laughing matter)
  • ((love / pride) no longer concerned her when she
    was elderly)
  • (her (charcoal-girl / soul) life saddened her)
  • (so she no longer flies (evil / shame)
  • she only sings out that (evil / pride devours /
    alternates-with hope / pride)))

35
14. Style
  • Style is fundamental to meaning
  • - not just way to present content
  • - not separate from content
  • - not surface, but deep in meaning
  • generation understanding
  • Model as choice of optimality principles for
    blending.

36
15. Future Work
  • More on optimality principles
  • - especially for structure
  • Semiotic blending for semiotic
  • spaces (with levels priorities)
  • Generalize architecture
  • - support interaction
  • for improvisation gaming
  • Are exploring a museum project
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