A Computational Model of Natural Language Communication 31 3. Data Structure and Algorithm 3.1 Proplets for Coding Propositional Content 3.1.1 C ONTEXT PROPLETS REPRESENTING dog barks. (I) run. 2 3 2 3 sur: sur: 2 3 sur: verb: bark verb: run noun: dog 6 7 6 7 6 7 6 7 6 7 arg: dog arg: moi 6 7 6 7 6 7 fnc: bark 6 7 6 7 4 5 nc: 23 run pc: 22 bark 4 5 4 5 prn: 22 prn: 22 prn: 23 3.1.2 C ODING OF RELATIONS BETWEEN CONCEPTS VIA PROPLETS sur: sur: sur: dog bark run verb: context level: noun: verb: arg: moi fnc: bark arg: dog pc: 22 bark prn: 22 nc: 23 run prn: 22 prn: 23 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 32 3.2 Internal Matching between Language and Context Proplets 3.2.1 L ANGUAGE PROPLETS REPRESENTING dog barks. (I) run. 2 sur: bellt 3 2 sur: fliehe 3 2 sur: Hund 3 verb: bark verb: run noun: dog 6 7 6 7 6 7 6 7 6 7 arg: dog arg: moi 6 7 6 7 6 7 fnc: bark 6 7 6 7 4 5 nc: 123 run pc: 122 bark 4 5 4 5 prn: 122 prn: 122 prn: 123 3.2.2 K EYS FOR LEXICAL LOOKUP IN THE SPEAKER - AND THE HEARER - MODE ← key for lexical lookup in the hearer-mode 2 3 sur: Hund ← key for lexical lookup in the speaker-mode noun: dog 6 7 6 7 fnc: 4 5 prn � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 33 3.2.3 Conditions on successful matching 1. Attribute condition The matching between two proplets A and B requires that the intersection of their attributes contains a predefined list of attributes regarded as relevant: {list} ⊆ {{proplet-A-attributes} ∩ {proplet-B-attributes}} 2. Value condition The matching between two proplets requires that the variables (and a fortiori the constants) of their common attributes are compatible. � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 34 3.2.4 I MPACT OF INTER - PROPLET RELATIONS ON MATCHING sur: bellt sur: fliehe bark run sur: Hund verb: verb: dog language level: noun: arg: dog arg: moi (horizontal relations) fnc: bark nc: 123 run pc: 122 bark prn: 122 prn: 122 prn: 123 internal matching (vertical relations) sur: sur: sur: dog bark run context level: noun: verb: verb: (horizontal relations) fnc: bark arg: dog arg: moi prn: 22 nc: 23 run pc: 22 bark prn: 22 prn: 23 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 35 3.3 Storage of Proplets in a Word Bank 3.3.1 D ATA STRUCTURE OF A WORD BANK context language recognition recognition bellt sur: sur: bellt bark verb: bark verb: bark arg: dog arg: dog prn: 22 prn: 122 frontier Hund sur: sur: Hund noun: dog noun: dog dog fnc: bark fnc: bark internal matching nc: 23 run nc: 123 bark prn: 22 prn: 122 sur: sur: fliehe fliehe verb: run verb: run run arg: moi arg: moi pc: 22 bark pc: 122 bark prn: 23 prn: 123 context language action action � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 36 3.4 Time-linear Algorithm of LA-Grammar 3.4.1 Applying the Input/Output Equivalence Principle to language 1. Input and output at the language level are signs of natural language, such as phrases, sen- tences, or texts. 2. The parts into which the signs of natural language disassemble during intake and discharge are word forms. 3. The order of the parts during intake and discharge is time-linear. � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 37 3.4.2 T IME - LINEAR D ERIVATION (P RINCIPLE OF P OSSIBLE C ONTINUATIONS ) Julia John knows lexical lookup verb: know noun: Julia noun: John arg: fnc: fnc: mdr: mdr: mdr: prn: prn: prn: syntactic−semantic parsing: verb: know noun: Julia arg: fnc: 1 mdr: mdr: prn: prn: 22 verb: know noun: John noun: Julia arg: Julia fnc: know fnc: 2 mdr: mdr: mdr: prn: 22 prn: 22 prn: result of syntactic−semantic parsing: verb: know noun: John noun: Julia arg: Julia John fnc: know fnc: know mdr: mdr: mdr: prn: 22 prn: 22 prn: 22 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 38 3.4.3 E XAMPLE OF AN LA-hear RULE APPLICATION rule name ss pattern nw pattern operations rule package » noun: α – » verb: β – copy α nw.arg rule level NOM+FV: {FV+OBJ, ...} fnc: arg: copy β ss.fnc 2 3 2 3 noun: Julia verb: know fnc: arg: proplet level 6 7 6 7 6 7 6 7 mdr: mdr: 4 5 4 5 prn: 22 prn: 3.4.4 R ESULT OF THE LA-hear RULE APPLICATION 2 3 2 3 noun: Julia verb: know fnc: know arg: Julia 6 7 6 7 6 7 6 7 mdr: mdr: 4 5 4 5 prn: 22 prn: 22 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 39 3.4.5 N ON - TIME - LINEAR D ERIVATION (P RINCIPLE OF P OSS . S UBSTITUTIONS ) S NP VP phrase structure derivation V NP Julia knows John lexical lookup verb: know noun: Julia noun: John num: sg tense: pres num: sg gen: fem subj: gen: masc obj: verb: know tense: pres subj: unification obj: noun: John num: sg gen: masc result verb: know tense: pres subj: noun: Julia num: sg gen: fem obj: noun: John num: sg gen: masc 3.5 Cycle of Natural Language Communication � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 40 3.5.1 E XAMPLE OF AN LA-think RULE APPLICATION rule name ss pattern nw pattern operations rule package 2 3 2 3 verb: β noun: α output position ss rule level V N V: arg: X α Y fnc: β {V N V, ...} 4 5 4 5 mark α ss prn: k prn: k 2 3 verb: know arg: Julia John proplet level 6 7 6 7 mdr: 4 5 prn: 22 3.5.2 R ESULT OF THE LA-think RULE APPLICATION 2 3 2 3 verb: know noun: Julia arg: !Julia John fnc: know 6 7 6 7 6 7 6 7 mdr: mdr: 4 5 4 5 prn: 22 prn: 22 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 41 3.5.3 S CHEMATIC PRODUCTION OF Julia knows John. activated sequence realization i V i.1 n n V N i.2 fv n n fv V N i.3 fv n n n fv n V N N i.4 fv p n n n fv n p V N N � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 42 3.5.4 T HE CYCLE OF NATURAL LANGUAGE COMMUNICATION hearer−mode speaker−mode recognition LA−hear LA−think LA−think sign context language context language proplets proplets proplets proplets action LA−speak � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 43 3.6 A Bare Bone Example of Database Semantics: DBS-letter 3.6.1 Isolated proplets representing the letters A, E, L, O, S, V 2 3 2 3 2 3 2 3 2 3 2 3 lett: A lett: E lett: L lett: O lett: S lett: V prev: prev: prev: prev: prev: prev: 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 next: next: next: next: next: next: 4 5 4 5 4 5 4 5 4 5 4 5 wrd: wrd: wrd: wrd: wrd: wrd: 3.6.2 D EFINITION OF LA-letter-IN FOR CONNECTING ISOLATED PROPLETS ST S = {(lett: α , {r-in})} 2 3 2 3 lett: α lett: β 5 copy α nw.prev r-in: prev: prev: {r-in} 4 5 4 copy β ss.next next: next: ST F = {(lett: β , rp r − in ) } � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 44 3.6.3 Example of an LA-letter-IN rule application rule name ss pattern nw pattern operations rule package 2 3 2 3 lett: α lett: β copy α nw.prev rule level r-in: prev: prev: {r-in} 4 5 4 5 copy β ss.next next: next: 2 3 2 3 lett: L lett: O prev: prev: proplet level 6 7 6 7 6 7 6 7 next: next: 4 5 4 5 wrd: wrd: 3.6.4 Result of the rule application 3.6.3 2 3 2 3 lett: L lett: O prev: prev: L 6 7 6 7 6 7 6 7 next: O next: 4 5 4 5 wrd: 1 wrd: 1 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 45 3.6.5 Time-linear derivation connecting the letters of love L O V E input lexical lookup lett: L lett: O lett: V lett: E prev: prev: prev: prev: sequence of isolated proplets next: next: next: next: wrd: wrd: wrd: wrd: syntactic−semantic parsing: lett: L lett: O connecting prev: prev: 1 proplets next: next: wrd: 1 wrd: lett: L lett: O lett: V connecting prev: prev: l prev: proplets 2 next:O next: next: wrd: 1 wrd: 1 wrd: connecting lett: L lett: O lett: V lett: E 3 prev: prev: L prev:O prev: proplets next:O next:V next: next: wrd: 1 wrd: 1 wrd: 1 wrd: result of syntactic−semantic parsing: lett: L lett: O lett: V lett: E prev: prev:L prev:O prev:V next:O next:V next: E next: wrd: 1 wrd: 1 wrd: 1 wrd: 1 � 2006 Roland Hausser c
A Computational Model of Natural Language Communication 46 3.6.6 Proplets for LOVE, LOSS, and ALSO in a Word Bank owner records member records 2 3 lett: A prev: 6 7 ˆ ˜ lett: A 6 7 next: L 4 5 wrd: 3 2 3 lett: E prev: V 6 7 ˆ ˜ lett:E 6 7 next: 4 5 wrd: 1 2 3 2 3 2 3 lett: L lett: L lett: L prev: prev: prev: A ˆ ˜ 6 7 6 7 6 7 lett:L 6 7 6 7 6 7 next: O next: O next: S 4 5 4 5 4 5 wrd: 1 wrd: 2 wrd: 3 � 2006 Roland Hausser c
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