formalization and implementation of cognitive semantics

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Implementation of Implementation of Cognitive Cognitive Semantics Semantics Joseph A Goguen Computer Science & Engineering University of California at San Diego Thanks to Fox Harrell for help with

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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. 1. Introduction. - PowerPoint PPT Presentation

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Page 1: Formalization and Implementation of  Cognitive Semantics

Formalization and Formalization and Implementation of Implementation of

Cognitive SemanticsCognitive Semantics

Joseph A Goguen

Computer Science & Engineering

University of California at San Diego

Thanks to Fox Harrell for help with slides & research.

Page 2: Formalization and Implementation of  Cognitive Semantics

1. Introduction1. Introduction

How to design human friendly ontologies?How to design human friendly ontologies? Mathematics, physics, formal philosophy Mathematics, physics, formal philosophy

are not always friendly!are not always friendly!

- “top down” & often counter-intuitive. - “top down” & often counter-intuitive.

- also culture specific- also culture specific

- Barry Smith, John Sowa, Robert Kent- Barry Smith, John Sowa, Robert Kent Most real ontologies built “bottom up” Most real ontologies built “bottom up”

- B2B, ecology (EML), etc.- B2B, ecology (EML), etc.

Page 3: Formalization and Implementation of  Cognitive Semantics

1. Introduction1. Introduction

Why not use cognitively real constructs? Why not use cognitively real constructs? - basic level concepts - basic level concepts

- basic image schemas - basic image schemas

- combine with blending, etc.- combine with blending, etc.

- especially good for spatial ontologies.- especially good for spatial ontologies. Evidence favors “middle-out” as humanEvidence favors “middle-out” as human

- See work of Rosch below.- See work of Rosch below.

Page 4: Formalization and Implementation of  Cognitive Semantics

2. Goals & Methods 2. Goals & Methods of Cognitive Semanticsof Cognitive Semantics

Goals:Goals:- Understand language/mind/body interface- Understand language/mind/body interface- Understand concepts & meaning- Understand concepts & meaning

- Understand how mind works- Understand how mind works Methods:Methods:

- Careful analysis of large bodies of language - Careful analysis of large bodies of language

(spoken, written, graphics) (spoken, written, graphics) - Introspection (member’s competance)- Introspection (member’s competance)

Page 5: Formalization and Implementation of  Cognitive Semantics

3. Rosch Experiments on 3. Rosch Experiments on Human ConceptsHuman Concepts

In “is_a” hierarchy, In “is_a” hierarchy, basic levelbasic level is in middle, is in middle, has shortest name, most rapid has shortest name, most rapid identification, most associated knowledge, identification, most associated knowledge, earliest learnedearliest learned

- since has most human interaction- since has most human interaction Highest level such that Highest level such that prototypeprototype exists, exists,

image representing whole category; image representing whole category; similar motor actions for interaction with similar motor actions for interaction with all instances.all instances.

Page 6: Formalization and Implementation of  Cognitive Semantics

3. Human Concepts3. Human Concepts

Examples:Examples:

- shoe, not footwear, or sneakers- shoe, not footwear, or sneakers

- apple, not fruit, or Macintosh- apple, not fruit, or Macintosh

- PC, not machine, or Macintosh- PC, not machine, or Macintosh Basic level concepts have maximal Basic level concepts have maximal

amount of internal structureamount of internal structure

- Could vary with user community- Could vary with user community

Page 7: Formalization and Implementation of  Cognitive Semantics

4. Conceptual Spaces, 4. Conceptual Spaces, Frames & DomainsFrames & Domains

Fauconnier Fauconnier mental spacesmental spaces are first order are first order relational structures (mostly binary)relational structures (mostly binary)

But theories are better: declarations & But theories are better: declarations & axiomsaxioms

FrameFrame is densely interconnected system of is densely interconnected system of concepts concepts - Family father, mother, son, daughter, …- Family father, mother, son, daughter, …- Chair with legs, seat, back, …- Chair with legs, seat, back, …

DomainDomain is larger collection of more loosely is larger collection of more loosely connected concepts (e.g., law, education)connected concepts (e.g., law, education)

Page 8: Formalization and Implementation of  Cognitive Semantics

5. Lakoff Metaphor Theory5. Lakoff Metaphor Theory

Image SchemasImage Schemas embodied & gestalt embodied & gestalt

- Container- Container

- Journey- Journey

- In/Out (is blend of two above)- In/Out (is blend of two above) Examples:Examples:

- He is trapped in his confusion.- He is trapped in his confusion.

- I don’t know where I’m going anymore.- I don’t know where I’m going anymore.

- She can’t get out of her old habits.- She can’t get out of her old habits.

Page 9: Formalization and Implementation of  Cognitive Semantics

5. Lakoff Metaphor Theory5. Lakoff Metaphor Theory

MetaphorMetaphor is conceptual space map is conceptual space map

- map is asymmetric: - map is asymmetric:

concrete source to abstract targetconcrete source to abstract target

- map is partial: not all source used- map is partial: not all source used

- understand target via source- understand target via source

- both entities & inferences mapped- both entities & inferences mapped

Page 10: Formalization and Implementation of  Cognitive Semantics

ExamplesExamples

MetaphorMetaphor - “The sun is a king”- “The sun is a king” - “Theories are constructed objects”- “Theories are constructed objects”

MetonymyMetonymy: one thing stands for another : one thing stands for another e.g., part for wholee.g., part for whole - “Paris disapproves of our Iraq policy”- “Paris disapproves of our Iraq policy”

- Is - Is notnot map, but internal to one space map, but internal to one space

Page 11: Formalization and Implementation of  Cognitive Semantics

An Extended ExampleAn Extended Example

““Theories are constructed objects”Theories are constructed objects”- Major premises are - Major premises are foundationsfoundations

- Major claims & arguments are - Major claims & arguments are structurestructure - Facts are - Facts are material constituentsmaterial constituents - Arguments are - Arguments are mortarmortar of facts & claims of facts & claims

- Logical strength is - Logical strength is designdesign or or architecturearchitecture- Theorist is - Theorist is architectarchitect- Believability is - Believability is strengthstrength- Persistence is - Persistence is successful standingsuccessful standing- Failure is - Failure is collapsecollapse

Page 12: Formalization and Implementation of  Cognitive Semantics

6. Fauconnier &Turner6. Fauconnier &TurnerConceptual BlendingConceptual Blending

Conceptual Space Networks Conceptual Space Networks Simple blend diagram: input spaces & Simple blend diagram: input spaces &

generic spacegeneric space

Page 13: Formalization and Implementation of  Cognitive Semantics

Conceptual BlendingConceptual Blending

Some strong claims for blending:Some strong claims for blending:

- is foundation of human thought- is foundation of human thought

- including reasoning & perception- including reasoning & perception

- is unconscious & rapid - is unconscious & rapid But are But are manymany choices for blending choices for blending

- so optimality principles are needed - so optimality principles are needed

to decide among them.to decide among them.

Page 14: Formalization and Implementation of  Cognitive Semantics

Houseboat ExampleHouseboat Example

Page 15: Formalization and Implementation of  Cognitive Semantics

Boathouse Blend SpaceBoathouse Blend Space

Page 16: Formalization and Implementation of  Cognitive Semantics

More ExamplesMore Examples

48 major blends for “house” & “boat”!48 major blends for “house” & “boat”! OxymoronsOxymorons

- Military intelligence- Military intelligence- New classic- New classic- Microsoft works- Microsoft works

CounterfactualsCounterfactuals- “In South Africa, Watergate wouldn’t - “In South Africa, Watergate wouldn’t

have done Nixon any harm.”have done Nixon any harm.”- “If I were you, I’d do nit now.”- “If I were you, I’d do nit now.”

Page 17: Formalization and Implementation of  Cognitive Semantics

7. Fauconnier & Turner7. Fauconnier & TurnerMetaphor TheoryMetaphor Theory

Use blending not mappingUse blending not mapping Cross space map emergent from Cross space map emergent from

what’s in blend spacewhat’s in blend space New emergent structure (see below)New emergent structure (see below) Main optimality principle: Relations Main optimality principle: Relations

compressed to human scalecompressed to human scale

Page 18: Formalization and Implementation of  Cognitive Semantics

Example: Climbing MonksExample: Climbing Monks

Page 19: Formalization and Implementation of  Cognitive Semantics

8.8. Common Sense Optimality PrinciplesCommon Sense Optimality PrinciplesAll are very informal: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.

Page 20: Formalization and Implementation of  Cognitive Semantics

Formal Optimality PrinciplesFormal Optimality Principles

Type preservationType preservation Arity (number of arguments)Arity (number of arguments) Axiom preservationAxiom preservation Level & priority preservationLevel & priority preservation

These can be checked by computer:These can be checked by computer:

They are implementable.They are implementable.

Page 21: Formalization and Implementation of  Cognitive Semantics

9. Promise & Problems9. Promise & Problems

New DevelopmentsNew Developments- Experimental studies of gesture- Experimental studies of gesture- Computer models of spatial - Computer models of spatial

prepositions, verb, modes, image prepositions, verb, modes, image schemas, using Petri netsschemas, using Petri nets

Dynamic, exciting field, relevant to Dynamic, exciting field, relevant to many other fieldsmany other fields

Page 22: Formalization and Implementation of  Cognitive Semantics

Problems with Conceptual Spaces:Problems with Conceptual Spaces:- Space cannot change over time- Space cannot change over time

- No constructors for structure- No constructors for structure

- Fixed common sense optimality - Fixed common sense optimality

principlesprinciples

- But need disoptimality & multi- - But need disoptimality & multi-

grain optimality principles (see below)grain optimality principles (see below)

Page 23: Formalization and Implementation of  Cognitive Semantics

Examples for New PrinciplesExamples for New PrinciplesMany modern poets go against what Many modern poets go against what

readers (used to) expect, e.g., Neruda:readers (used to) expect, e.g., Neruda:

“ “I am withered, impervious, like a swan of feltI am withered, impervious, like a swan of felt

navigating a water of beginning and ashes.”navigating a water of beginning and ashes.”

Or Rilke:Or Rilke:

“ “cheap winter hats of fate”cheap winter hats of fate”

For this, need For this, need disdisoptimality principlesoptimality principles

Also structure at multiple granularitiesAlso structure at multiple granularities

Page 24: Formalization and Implementation of  Cognitive Semantics

10. Extensions10. Extensions Conceptual blending good for language, Conceptual blending good for language,

but needs extending for other mediabut needs extending for other media Such as: Such as:

- Computational narrative- Computational narrative

- User-interface design- User-interface design

- Gaming- Gaming

- Database Integration, Querying- Database Integration, Querying

Page 25: Formalization and Implementation of  Cognitive Semantics

Three Levels of LangugeThree Levels of Languge

DiscourseDiscourse SentenceSentence Phrase (Including metaphor)Phrase (Including metaphor)

Treated differently in our generative Treated differently in our generative system for pragmatic purposes, but system for pragmatic purposes, but are not really distinctare not really distinct

Page 26: Formalization and Implementation of  Cognitive Semantics

11. Labov Narrative Structure11. Labov Narrative Structure

Structure of narratives of personal experience, Structure of narratives of personal experience, work of William Labov & Charlotte Linde:work of William Labov & Charlotte Linde:

- Optional orientation section gives time, place, - Optional orientation section gives time, place, characters, etc.characters, etc.

- Narrative clauses describe events, by default, - Narrative clauses describe events, by default, occur in same order as in storyoccur in same order as in story

- Narrative clauses interwoven with evaluative - Narrative clauses interwoven with evaluative material, are interpretative or evaluative material, are interpretative or evaluative informationinformation

- Optional closing section summarizes story or - Optional closing section summarizes story or gives moral.gives moral.

Page 27: Formalization and Implementation of  Cognitive Semantics

Labov Structure in Extended BNFLabov Structure in Extended BNF <<Narr> ::= <Open> (<Cls> <Eval>*)* [<Coda>] Narr> ::= <Open> (<Cls> <Eval>*)* [<Coda>]

<Open> ::= ((<Abs> + <Ornt>) <Eval>*)*<Open> ::= ((<Abs> + <Ornt>) <Eval>*)*

We can also use other narrative structure We can also use other narrative structure

grammars for top level of generation systems, grammars for top level of generation systems,

e.g., postmodern, jumpcut, flashback, …e.g., postmodern, jumpcut, flashback, …

Page 28: Formalization and Implementation of  Cognitive Semantics

12. Algebraic Semiotics12. Algebraic Semiotics Semiotic spaces consist of sorts, Semiotic spaces consist of sorts,

relations, axioms & constants, with relations, axioms & constants, with partial order on each, & primary sortpartial order on each, & primary sort

Semiotic morphisms are partial maps Semiotic morphisms are partial maps between semiotic spacesbetween semiotic spaces

““Algebraic semiotics” is ‘brand name’ Algebraic semiotics” is ‘brand name’ not aligned with contemporary not aligned with contemporary semiotics, though influenced by Peirce semiotics, though influenced by Peirce & Saussure& Saussure

Page 29: Formalization and Implementation of  Cognitive Semantics

Builds on algebraic semantics & abstract Builds on algebraic semantics & abstract data type theorydata type theory

Users insights from cognitive linguistics Users insights from cognitive linguistics & conceptual blending& conceptual blending

Nice math definition of blending: Nice math definition of blending: lax colimit in enriched category (3/2 lax colimit in enriched category (3/2

colimit in 3/2 category)colimit in 3/2 category) Assumes ordering on morphismsAssumes ordering on morphisms as way to determine best blendsas way to determine best blends

Page 30: Formalization and Implementation of  Cognitive Semantics

Data Structure for Data Structure for Conceptual BlendingConceptual Blending

Page 31: Formalization and Implementation of  Cognitive Semantics

13. Structural Blending13. Structural Blending

Generative media need Generative media need structurestructure, not , not just concepts about structure (e.g., just concepts about structure (e.g., for syntax & discourse)for syntax & discourse)

““Templates” act as constructors Templates” act as constructors (which are functions)(which are functions)

Blending is textual substition & thenBlending is textual substition & then

cleaning up – but we can do bettercleaning up – but we can do better

in the futurein the future

Page 32: Formalization and Implementation of  Cognitive Semantics

Active Poetry SystemActive Poetry System

Page 33: Formalization and Implementation of  Cognitive Semantics

The Girl with Skin of Haints and Seraphs

her tale began when she was infected with scaled-being first-borntisfemale oppressed vapor steamed from her pores when she rode her

bicycledeath was bettershe fears only female spectresshe loves only black ghoststhey inspire herwhen she was no longer a child, Exu skin marks streaked her thighsher lips danced with love and pride.it was no laughing matterlove and pride no longer concerned her when she was elderlyher charcoal-girl soul life saddened herso she no longer flies with evil shame she only sings out that evil pride devours and alternates-with hope

pride.

Page 34: Formalization and Implementation of  Cognitive Semantics

((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)))

Page 35: Formalization and Implementation of  Cognitive Semantics

14. Style14. Style

Style is fundamental to meaning:Style is fundamental to meaning:

- not just way to present “content”- not just way to present “content”

- not separate from “content”- not separate from “content”

- not surface, but deep in meaning - not surface, but deep in meaning

generation & understandinggeneration & understanding

Model as choice of optimality Model as choice of optimality principles for blending.principles for blending.

Page 36: Formalization and Implementation of  Cognitive Semantics

15. Future Work15. Future Work

More on optimality principles More on optimality principles - especially for structure- especially for structure Semiotic blending for semiotic Semiotic blending for semiotic spaces (with levels & priorities)spaces (with levels & priorities) Generalize architectureGeneralize architecture - support interaction:- support interaction: for improvisation & gamingfor improvisation & gaming Are exploring a museum projectAre exploring a museum project