Formalization and Implementation of Cognitive Semantics

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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.
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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.

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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.

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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)

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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.

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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

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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)

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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.

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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

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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

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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

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6. Fauconnier TurnerConceptual Blending

• Conceptual Space Networks
• Simple blend diagram input spaces generic
  space

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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.

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Houseboat Example
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Boathouse Blend Space
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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.

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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

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Example Climbing Monks
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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.

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Formal Optimality Principles

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

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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

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• 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)

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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

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10. Extensions

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

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Three Levels of Languge

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

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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.

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• 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,

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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

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• 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

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Data Structure for Conceptual Blending
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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

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Active Poetry System
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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.

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• ((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)))

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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.

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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