Unified Cognitive Science Neurobiology Psychology Computer Science Linguistics Philosophy Social Sciences Experience Take all the Findings and Constraints Seriously

What are schemas? Regularities in our perceptual, motor and cognitive systems Structure our experiences and interactions with the world. May be grounded in a specific cognitive system, but are not situation-specific in their application (can apply to many domains of experience)

Basis of Image schemas Perceptual systems Motor routines Social Cognition Image Schema properties depend on Neural circuits Interactions with the world

Image schemas Trajector / Landmark (asymmetric) The bike is near the house ? The house is near the bike Boundary / Bounded Region a bounded region has a closed boundary Topological Relations Separation, Contact, Overlap, Inclusion, Surround Orientation Vertical (up/down), Horizontal (left/right, front/back) Absolute (E, S, W, N) LM TR bounded region boundary

Similarity: Perceptual and motor systems Basic functional interactions with the world Environment Variation: Cross-linguistic variation in how schemas are used.

Cross-linguistic Variations

English

Japanese

Tamil

English ON AROUND OVER IN Bowerman & Pederson

Dutch Bowerman & Pederson AAN OM BOVEN IN OP

Chinese Bowerman & Pederson SHANG ZHOU LI

Spatial schemas TR/LM relation Boundaries, bounded region Topological relations Orientational Axes Proximal/Distal

Trajector/Landmark Schema Roles: Trajector (TR) – object being located Landmark (LM) – reference object TR and LM may share a location (at)

TR/LM -- asymmetry The cup is on the table ?The table is under the cup. The skateboard is next to the post. ?The post is next to the skateboard.

Boundary Schema Region A Region B Boundary Roles: Boundary Region A Region B

Bounded Region Roles: Boundary: closed Bounded Region Background region

Topological Relations Separation

Topological Relations Separation Contact

Topological Relations Separation Contact Coincidence:

Topological Relations Separation Contact Coincidence: - Overlap

Topological Relations Separation Contact Coincidence: - Overlap - Inclusion

Topological Relations Separation Contact Coincidence: - Overlap - Inclusion - Encircle/surround

Orientation Vertical axis -- up/down up down above below upright

Orientation Horizontal plane – Two axes:

Language and Frames of Reference There seem to be three prototypical frames of reference in language (Levinson) Intrinsic Relative Absolute

Intrinsic frame of reference front back right left

Relative frame of reference front back left?? right??

Absolute frame of reference north west south east

TR/LM and Verticality Schemas The book is under the table. up down under

Proximal/Distal Schema.

Simple vs. Complex Schemas

Container Schema Roles: Interior: bounded region Exterior Boundary C

C C TR outin TR/LM + Container

Container Schema Elaborated Complexities –more roles/specifications: Boundary properties Strength Porosity Portals

Container schema logic C x A B

Source-Path-Goal Constraints: initial = TR at Source central = TR on Path final = TR at Goal SourcePath Goal

SPG -- simple example She drove from the store to the gas station. TR = she Source = the store Goal = the gas station SourcePath Goal

SPG and Container She ran into the room. SPG. Source ↔ Container.Exterior SPG.Path ↔ Container.Portal SPG. Goal ↔ Container.Interior

PATH landmarks past across along LM

Part-Whole Schema Part Whole

semantic schema Container roles: interior exterior portal boundary Representing image schemas Interior Exterior Boundary Portal Source Path Goal Trajector These are abstractions over sensorimotor experiences. semantic schema Source-Path-Goal roles: source path goal trajector

Language and Spatial Schemas People say that they look up to some people, but look down on others because those we deem worthy of respect are somehow “above” us, and those we deem unworthy are somehow “beneath” us. But why does respect run along a vertical axis (or any spatial axis, for that matter)? Much of our language is rich with such spatial talk. Concrete actions such as a push or a lift clearly imply a vertical or horizontal motion, but so too can more abstract concepts. Metaphors: Arguments can go “back and forth,” and hopes can get “too high.”

Regier Model Lecture Jerome A. Feldman February 27, 2007 With help from Matt Gedigian

Neural Theory of Language

Language Development in Children 0-3 mo: prefers sounds in native language 3-6 mo: imitation of vowel sounds only 6-8 mo: babbling in consonant-vowel segments 8-10 mo: word comprehension, starts to lose sensitivity to consonants outside native language mo: word production (naming) mo: word combinations, relational words (verbs, adj.) mo: grammaticization, inflectional morphology 3 years – adulthood: vocab. growth, sentence-level grammar for discourse purposes

Trajector/Landmark Schema Roles: Trajector (TR) – object being located Landmark (LM) – reference object TR and LM may share a location (at)

TR/LM -- asymmetry The cup is on the table ?The table is under the cup. The skateboard is next to the post. ?The post is next to the skateboard.

Language and Frames of Reference There seem to be three prototypical frames of reference in language (Levinson) Intrinsic Relative Absolute

Basis of Image Schemas Perceptual systems Motor routines Social Cognition Image Schema properties depend on Neural circuits Interactions with the world

Image schemas Trajector / Landmark (asymmetric) The bike is near the house ? The house is near the bike Boundary / Bounded Region bounded region has a closed boundary Topological Relations Separation, Contact, Overlap, Inclusion, Surround Orientation Vertical (up/down), Horizontal Absolute (E, S, W, N) LM TR bounded region boundary

Spatial schemas TR/LM relation Boundaries, bounded region Topological relations Orientational Axes Proximal/Distal

Regier’s Model Training input: configuration of TR/LM and the correct spatial relation term Learned behavior: input TR/LM, output spatial relation Learning System abovebelowleftrightinoutonoff Input: TR LM above

Issue #1: Implicit Negatives Children usually do not get explicit negatives But we won’t know when to stop generalizing if we don’t have negative evidence Yet spatial relation terms aren’t entirely mutually exclusive The same scene can often be described with two or more spatial relation terms (e.g. above and outside) How can we make the learning problem realistic yet learnable?

Dealing with Implicit Negatives Explicit positive for above Implicit negatives for below, left, right, etc in Regier: E = ½ ∑ i,p (( t i,p – o i,p ) * β i,p ) 2, where i is the node, p is the pattern, β i,p = 1 if explicit positive, β i,p < 1 if implicit negative

Learning System dynamic relations (e.g. into) structured connectionist network (based on visual system)

Topological Relations Separation Contact Coincidence: - Overlap - Inclusion - Encircle/surround

Issue #2: Shift Invariance Backprop cannot handle shift invariance (it cannot generalize from 0011, 0110 to 1100) But the cup is on the table whether you see it right in the center or from the corner of your eyes (i.e. in different areas of the retina map) What structure can we utilize to make the input shift-invariant?

Limitations Scale Uniqueness/Plausibility Grammar Abstract Concepts Inference Representation

Demo of the Regier System on the English above

Language and Thought We know thought (our cognitive processes) constrains the way we learn and use language Does language also influence thought? Benjamin Whorf argues yes Psycholinguistics experiments have shown that linguistics categories influence thinking even in non-linguistics task Language Thought cognitive processes