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 (member’s 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 don’t know where I’m going anymore. - She can’t 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 wouldn’t have done Nixon any harm.” - “If I were you, I’d do nit now.”

17. 7. Fauconnier & TurnerMetaphor Theory • Use blending not mapping • Cross space map emergent from what’s 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 <Narr> ::= <Open> (<Cls> <Eval>*)* [<Coda>] <Open> ::= ((<Abs> + <Ornt>) <Eval>*)* 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