Categorization PA116 – L5 (c) Zdenko Stanicek, Sept 2010 OPVK_MU_EN_stred_2.jpg 2 elementary_belief 3 Categorization by G. Lakoff - category as container •Term category is not a synonym for type! •Categories are containers, into/from which we insert/remove objects •Inserting objects into categories is called categorization •Level-of-detail and way-of-categorizing rely on a subject, which is doing the categorization and upon what basis it is done •Hierarchical taxonomy of categories: the order from the most general ones to the most specialized ones Example: Item of Technical Maintenance Oil-Transf. Dry-Transf. Device Transformer Electrical distributor Pillar Lightning arrester Bulk power substation Switchboard Cable Building ITM Hierarchical taxonomy of categories •Vertebrate –Mammal •Predator –Feline »Tiger 6 Which level in hierachical taxonomy is the most important one? •Classical theories: categories in the middle of taxonomy are not interesting •Lakoff: from the psychological point of view the basic level lays somewhere in the middle of the hierarchy Superior level animal furniture Basic level dog chair Subordinate level Labrador rocking chair 7 Basic level: •It is the uppermost level, on which shapes of elements of given category are perceived as the elements are alike •It is the uppermost level, on which a simple mental figure reflects all elements from given category •It is the uppermost level, on which a person uses nearly the same motoric actions when interacting with elements of given category •It is the level, on which are elements of given category identified the fastest by tested persons 8 Basic level in hierarchical taxonomy (once more) •Our perception is anchored by our human dimension •The reason of this can be explained by: •Enactive Perception: “a dialogue” of the perceiving person and the environment/neighbourhood Superior level animal furniture Basic level dog chair Subordinate level Labrador rocking chair 9 Preconceptions and facts •„Basic categories are objective“ •It is not true! : •Basic categories are only „human-sized“ •Categorizing depends on the way, how people interact with surrounding objects •… and not only on objects themselves and their attributes > 10 How we can categorize ? •Prototype categorizing (the base) •Metonymic categorizing •Use of Radial Categories Prototype categorizing •Tag notable elements •Abstract from details and declare them as “invariant representations” of a set of properties •Each element having the same or similar properties hook on the tagged elements •The tagged element together with all on it hooked elements form Category 12 Prototype categorizing – cont. •Some categories have embedded a graduation –Fuzzy borders –Central members = prototypes –Central member has a level of belongingness into category equal to 1 –Members distant from central ones has a level of belongingness into category smaller than 1 •E.g.: tall person, red •…this depends on Context, often … 13 „Tall person“ “Red” Prototype Categorizing - result •Select the ideal representative item •(This is the “invariant representation” of what we call “category”) •Express the fact that item I belongs to category C by connection (I, C) à c –where c is measure of certainty •Category is no more seen as a container, but it is seen as a hook (central member = prototype) to which we hang up other members 16 Reasons for Prototype categorizing •Some categories has their borders set, but some members are better examples than others •E.g.: bird: >>eagle, >>chicken, >>penguin •Basic level depends on perceived structure “whole-part” and on knowledge about how parts work with respect to the whole •Categories are not objective, nor independent on human being (not independent on categorizing agent). •For categories there are important attributes, so-called interaction attributes : characterizing interactions of human beings (agents) with their neighbourhood 17 The “T” elementary_belief 18 Context elementary_belief •(I, C, c = 1, a = amax) is a context. •Let T1, …, Tn be arbitrary elementary beliefs. Than (T1, …, Tn), i.e. a finite sequence of elementary beliefs is a context. 19 DIAM_2_cognitive_elements 20 Metonymy •„That appendix on four has fever again.“ •One easily perceivable aspect of the object/situation is used as a representation of the object/situation. •Typically: A member of another (but in a way connected) category is becoming metonymical representation of the whole category for reasoning purposes. •„White collars do not like to work by hands.“ 21 Radial categories •Central case = prototype member, clearly perceived by everyone •Many variations of this case, which cannot be specified by general rules •Example: “Mother” •Central case: woman, she gave a birth, feeds by breast a child, rises a child, loves her child, is wife of a father of a child, is older than a child for one generation •Variations: stepmother, adoptive mother, biological mother, mother-she Charley who lives with father-he Andrew, raven mother > 22 Influence on a way of thinking •Radial categories •Metonymically explicated categories •… what objects/items and which relationships we have to take into account, and which operations (distinguishing procedures) we have to execute to realize that something focused is e.g. „mother“ •Hence: category is not a primitive concept but a composite of relationships and operations (see the deep explication of the Diamond of focus) category is not a primitive concept: 24 Jeff Hawkins’ Hypotheses (in his book: “On Intelligence” ) •Neocortex stores sequences of patterns •Neocortex stores patterns in an invariant form (invariant representation) •A sequence of patterns is a pattern again •Neocortex stores patterns in a Hierarchy (see the Fundamental Hierarchy—Diamond of Attention—and substitute “pattern” for “object”) •Neocortex doesn’t distinguish between external inputs and internal inputs (the ratio ext : int is ?) •Thus: Concepts are invariant representations of sequences of (elementary) patterns. touch audition vision FUNDAMENTAL HIERARCHY A model of Fundamental Hierarchy pattern sequence 27 DIAM_2_cognitive_elements … and how we reason on this FH: … and now the role of CONCEPTUAL MODELING in the light of Lakoff categorization 29 OBJECT „which is focused on“ CONSTRUCTION linguistic EXPRESSION represents denotes identifies NLE analysis Why do we understand each other while talking? How is it possible we can translate from one language to another? 30 Attention Focusing •Modeling process (of a given Domain) is similar to a focusing of a camera objective when making photos: in front of the objective there is everything while the photo depicts clearly only these things which are focused on. •This means: –over EB we choose particular types and we focus our attention to objects belonging to this types only –the model than contains constructions of these focused objects •The focused objects are: HIT attributes and sorts 31 Hierarchy of types for DM •E-types, D-types •node types •tuple types •basic types •Instances of H-types E-types type Bool Instances of H-types basic types constructed over node types tuple types D-types 32 H-types •Let T1,...,Tn are node types (not necessarily diverse), at least one of them is an E-type. •Let S is arbitrary basic type •H-type is each type of the form (a) (Wrd  (Tim  ((T1, ..., Tn)  S))) or (b) (Wrd  (Tim  ((T1, ..., Tn)  (S  Bool)))) (in case (b) the S must not be the Bool) 33 HIT-attributes •If A is an object of H-type i.e. A / (Wrd  (Tim  ((T1, ..., Tn)  S))) or A / (Wrd  (Tim  ((T1, ..., Tn)  (S  Bool))))‏ •then object A is called HIT-attribute. •Each HIT-attribute is an intenzion. •HIT-attribute A is constructed by wt x1...xn y ([Awt(x1,,..., xn)] = y) in case (a) and wt x1...xn y [[Awt(x1, ..., xn)] y] in case (b) 34 Recording the semantics •A / (Wrd  (Tim  ((T1, ..., Tn)  S))) •A = text0(S) text1 (T1) text2 (T2) ... textn (Tn) textn+1 •where text0 and textn+1 can be omitted, only, and the whole NL expression denotes a function which returns values from S on arguments from the tuple type (T1, ..., Tn) •And the corresponding semantic diagram … 35 Recording the semantics •A / (Wrd  (Tim  ((T1, ..., Tn)  (S  Bool)))) •A = text0(S)-s text1 (T1) text2 (T2) ... textn (Tn) textn+1 •where text0 and textn+1 can be omitted, only, and the whole NL expression denotes a function which returns values from 2S on arguments from the tuple type (T1, ..., Tn) (suffix -s distinguishes from the case (a) and tells us to read the expression using plural) And the corresponding semantic diagram … Example: Operative and Tactical Marketing business_plan_mind_model •Name of Sort: complex solutions producer Type: Kernel Super-Type: subject An object from the category (#complex solutions producer) is each subject which composes several products and solutions into a complex product. This product the complex solutions producers provide/supply to its customers. Particular solutions or products embedded in this complex product are invisible by their brands to end-customers. •Name of Sort: customer Type: Kernel An object from the category (#customer) is every end customer who is or can be a consumer or user of our services or products. It is an agent acting on the market, which is autonomous and co-operative in a sense of holonic approach, to which attention can be reasonably paid. •Name of Sort: negotiated deal Type: Associative An object from the category (#negotiated deal) is each representation of a relationship between (#solution), (#customer), (#customer pain/need) and (#subject) with the meaning: results (text description) achieved by given (#subject) while using given (#solution) for curing given (#customer pain/need) by a sale to given (#customer) / 0,1:0,M •Name of Connection: 2: curing Cardinality: customer pain/need -> solution: 0,M, reversely: 0,M Connection between entities customer pain/need and solution with the following meaning (#solution)-s curing given (#customer pain/need) / 0,M:0,M Lesson learnt: •Try to understand a phenomenon/situation/structure/ environment/behavior/… means: •Plan and execute a Project •The crucial part of a definition of the Project is: •The Objective = Triple Constraint Lesson learnt: •Triple Constraint is –What –When –For How Much •The key part of it is the “What” •The What is described in PM domain by the so called WBS Lesson learnt – the point ! •Conceptual model is a special way to define a “WBS” of the particular problem: “to UNDERSTAND the given DOMAIN”. •This is an objective specification! •Draw the CM in a form of WBS! see the model from lesson 1