A parsimonious Begriffsschrift

[concept notation] for animals

James R Hurford

PHILOSOPHY

speculative, armchair

Deep and careful

reasoning

NEUROSCIENCE

empirical, laboratory

Rigorous controlled

experiments

x (W(x) y (M(y) →L(x,y)))

A) V E

Pragmatics+Semantics

Morphosyntax

Phonology

Phonetics

SOUNDS

MEANINGS

Phonetic transcription: [bru:thus khaizarem nekhawit]

Logical form (e.g. FOPL): Stab(e) & Agent(e,brutus) & Patient(e,caesar)

Phonetics

Acoustic form Motor commands

Semantics

Universe of discourse Mental representations

STARSEARTHHOMEPERSONTOENAIL

Crack open a brain, and what do you find?

No symbols!

The nature of mental representations

Symbolic notations are useful.

“The grasp schema.

1. The role parameters: agent, object, object location, and the action itself.

2. The phase parameters: initial condition, starting phase, central phase, purpose condition, ending phase, final state.” (Gallese & Lakoff, 2005)

“… we have written down symbols (e.g. final state) as our notation for functional clusters. This does not mean that we take functional clusters themselves to be symbolic. The symbols are only our names for functional clusters, which function as neurally realised units” (Gallese & Lakoff, 2005)

A phonetic analogy

SymbolsNon-symbolic

represent-ations

Frege devised a Begriffschrift, a symbolic notation for writing concepts.

This has become First Order Predicate Logic (FOPL).

It is useful to linguists and logicians for representing the meanings of sentences.

Frege, and many modern logicians, posit abstract, non-neural status for their symbols.

The (new) research programme is to develop a symbolic notation for the meanings of sentences with a natural neural interpretation.

The proposed notation builds on

Event-based semantics (Davidson,1967; Parsons, 1990)

Discourse Representation Theory (Kamp & Reyle, 1993)

Conjunctivism (Batali, 2002; Pietroski, 2005)

How this relates to language evolution

Higher animals have no language, but they have private conceptual representations of the world, implemented in functional neural clusters.

Apes and humans share many aspects of the neural representation of scenes.

These are the primitive basis of later evolved public language.

Linguistic/logical formulae are cluttered with entities of too many different kinds.

• Predicates - 1-place, 2-place, 3-place, …

Individual constants

Individual variables

Quantifiers

Role Markers

Connectives

RED, MAN, HIT, GIVE

John, London

x, y, z

,

Agent, Patient, …

&, V, ~

Occam’s razor – a parsimonious entity set for linguistic/logical formulae

• Predicates - 1-place

Individual variables, up to 4

Quantifier (implicit)

Connective (implicit)

RED, MAN, (HIT, GIVE),

JOHN, LONDON

AGENT, PATIENT, …

w, x, y, z

&

Reminder: the representations I propose face two ways: they are convenient symbolic notations (names) …

1.… for linguists and logicians to map onto (a subset of) human language sentences.

2. … to express the neural patterns constituting pre-linguistic thoughts (e.g. in animals and babies).

Therefore, they must meet both linguistic and neural criteria of adequacy.

An unproblematic example

( x y)

DOG(x) & BROWN(x) & CAT(y) & WHITE(y)

Ci sono un cane marrone ed un gatto bianco

Three notational moves:

• Individual constants (proper names) as predicates

• Role markers (Agent, Patient, …) as predicates

• Reducing all predicates to 1-place

Three philosophical themes:

• Abandoning the God’s-eye-view of logic

• Objects in cognition as bundles of features

• Events, scenes, situations are complex objects

Three neuropsychological phenomena:

• Dorsal-ventral separation

• Global and local attention (– simultanagnosia, etc)

• Frame of reference systems

Proper names are proto-logically predicates: the principled unknowability of uniqueness.

FIDO(x) & FELIX(y)

Reminder: Predicate symbols, e.g. CAT, FIDO, “are only our names for functional clusters, which function as neurally realised units.” (Gallese & Lakoff, 2005)

PredictionThere is no agnosia or anomia that affects all and only non-proper names, i.e. affects predicates but not individual constants.

PREDICATESIndividual constants

Animal predicates

Vegetable predicates

Fruit predicates Tool

predicates

Personal name

predicates

x y

Jones(x)

Ulysses(y)

x owns y

Kamp & Reyle, 1993, p.64

Precedent in Discourse Representation Theory

Participant roles (aka theta roles) e.g. Agent, Patient, etc. are predicates.

They just happen to be predicates typically expressed by grammatical relations, e.g. Subject, Direct Object, Indirect Object, rather than by words.

But many roles are signalled by particular words, e.g.

Agent -- by, do, leader Patient -- victim

Beneficiary -- to, get Instrument -- with, use

Locative -- in, at, on

Event semantics (e.g. Parsons, 1990) treats Agent, Patient, etc. as predicates and event verbs as 1-place.

e STAB(e) & AGENT(brutus,e) & PATIENT(caesar,e)

With proper names as predicates:

e STAB(e) & AGENT(x, e) & PATIENT(y, e)

& BRUTUS(x) & CAESAR(y)

The original 2-place predicate STAB is now 1-place, and AGENT and PATIENT have become 2-place.

Valency (arity) is debatable.

Reducing all predicates to 1-place

Motivation: Hurford (2003) claims a correspondence

• between indices for external objects of focal attention, delivered by the dorsal stream, and individual variables w, x, y, z; and

• between categorical judgements about objects’ properties, delivered by the ventral stream, and predicates, such as RED, CAT, MARY.

The brain integrates what these two streams deliver into a single PREDICATE(x) representation.

The 1-place claim is not so radical as it may seem.

In event semantics, the roles (Agent, Patient, etc.) are only 2-place to link them to the event predicate.

e STAB(e) & AGENT(x, e) & PATIENT(y, e)

& BRUTUS(x) & CAESAR(y)

A box notation can likewise relativize the role predicates to the event predicate.

STABAGENT

BRUTUS

CAESAR

PATIENT

e STAB(e) & AGENT(x, e) & PATIENT(y, e)

& BRUTUS(x) & CAESAR(y)

In the box notation:

• Each box is the equivalent of a separate individual variable, x, y, z, …

• The predicates inside a box are equivalent to conjunctions of predicates applying to the variables.

• Items within boxes are unordered.

STABAGENT

BRUTUS

CAESAR

PATIENT

Role predicates are assigned relative to their event contexts.

Dowty’s Proto-Agent and Proto-Patient. A participant can have more or fewer of the prototypical properties of an Agent, e.g. animacy, movement, volition, causation.

What is an Agent for one event (e.g. running) could be a Patient for another event (e.g. chasing).

Predicates are more or less context-relative:

gradable predicates, e.g. BIG

common nouny predicates, e.g. HERO,TABLE

proper nouny predicates, e.g. JOHN, LONDON

Frame of Reference

Judgements are made relative to their contexts.

E.g. Input judged as WHITE in half-light is judged as GREY in full light.

Jokisch & Troje (2003) Fast-striding animals are seen as relatively small, and slow-striding animals are judged to be relatively big.

Sarris (1998) Chickens can be trained to make perceptual judgements such as ‘big for a red cube’ and ‘small for a green cube’.

Jones

Ulysses

owns

x y

Kamp & Reyle, 1993, p.64

(x)

(y)

person book

yx

In any (non-symmetric) 2-place predication, one argument is always distinguished from the other by some property (1-place). That’s how we can tell which role each argument plays.

In symmetric 2-place predications, both arguments have the same role properties.

MEET (john, mary) = MEET (mary, john)

In the traditional notation, argument ordering is superfluous.

JOHN MARY

MEET

Global and local attention

“Forest before trees” – “global structuring of a visual scene precedes analysis of local features” (Navon, 1977:353)

“An initial rapid pass through the visual hierarchy provides the global framework and gist of the scene and primes competing identities through the features that are detected. Attention is then focused back to early areas to allow a serial check of the initial rough bindings and to form the representations of objects and events that are consciously experienced.” (Treisman, 2004:541)

• Global attention searches for individual features in a scene in parallel. Individual features (e.g. RED) pop out.

• Local attention fixes serially on separate objects, up to about 4, binding their conjunctions of features, (e.g. BLUE RED

SQUARE , UP

ARROW )

• These two separate process integrate seamlessly in normal vision (and hearing) to provide a single unified representation of a scene.

Disorders involving global or local attention• Simultanagnosia: patients “can only see one object at a time”, and “cannot make sense of pictures of familiar scenes”.

• Williams Syndrome: impaired global attention

• Down Syndrome: impaired local attention

• Left neglect: failure of orienting response to left visual field

+

Global and local attention

REDYELLOW

PURPLE

SKIRT

DANCE

GIRLGIRL

Quick global attention delivers something like

with predicates only approximately bound

Global and local attention

Another example

KISS

BOY

GIRL

SMILE

Quick global attention delivers

An iconic notation, taking a cue from event semantics

KISS

AGENT BOY

PATIENT GIRL

SMILE

KISS(e) & AGENT(x) &

BOY(x) & PATIENT(y) & GIRL(y) &

SMILE(y)

Boxes correspond to individual variables, e, w, x, y, z.

An iconic notation, taking a cue from event semantics

AGENT GIRL

SMILE

AGENT(y) & GIRL(y) & SMILE(y)

(No ontological distinction between a one-participant event/state and an individual object.)

In relation to the box notation:

• Whole event/scene/situation predicates are those delivered by global attention, unbound to any particular object in the scene. Such a predicate goes in the outer box.

• Such whole-scene predicates can select for scenes with particular numbers of participants.

CHURCHILL

ROOSEVELT

STALIN

THREE

CHURCHILL LEFT

ROOSEVELT MIDDLE

STALIN RIGHT

BETWEEN

A “betweenness situation” necessarily involves three participants.

FACE

PARTEYE

BLUE

PARTEYE

BLUE

PART NOSE

CROOKED

A face with two blue eyes and a crooked nose.

These are private scene representations; aspects of meaning involving public communication are not represented. E.g.

• Active/passive pairs:– Kanzi gave Matata a banana– Matata was given a banana by Kanzi– A banana was given to Matata by Kanzi

• Various Topicalization devices:– Kanzi bit Matata– Matata, Kanzi bit her– It was Matata that Kanzi bit

• Some relative clause or modifying structures:– Kanzi bit the chimp that was screaming– Kanzi bit the screaming chimp– The chimp that Kanzi bit was screaming– The screaming one that Kanzi bit was a chimp

THE ENDThanks for listening.