Davidsonian Logic Forms

Stuff

predicates

• a predicate is generated for every noun, verb, adjective or adverb in the sentence
• the name of a predicate includes the base form, and part-of-speech
• for example:
  • A learner is enrolled in an educational institution
  • has predicates: (learner:n, enroll:v, educational_institution:n)

Predicate Arguments

• all verb predicates, as well as the nominalization representing actions, events or states have three arguments:
• action/static/event_predicate (𝑒_𝑖, 𝑥_𝑗, 𝑥_𝑘), where:
  • 𝑒_𝑖 represents the action, state or event 𝑖
  • 𝑥_𝑗 represents the syntactic subject 𝑗 of 𝑒_𝑖
  • 𝑥_𝑘 represents the syntactic direct object 𝑘 of 𝑒_𝑖
• for example:

modifiers

• predicates generated from modifiers share the same arguments with the predicates corresponding to the phrase heads.
• for example:
  • adjectives have same predicates as nouns:
    • a manmade object
    • object:n(𝑥₁) & man-made:a(𝑥₁)
  • adverbial predicate is the eventuality of the verb it modifies
    • run quickly
    • run:v(𝑒₁, 𝑥₁, 𝑥₂) & quickly:r(𝑒₁)

conjunctions

• conjunctions are transformed in predicates.
• conjunction predicates have a variable number of arguments

examples:

• An achievement demonstrating great skill or mastery

• achievement:n(x1) & demonstrate: v(e1,x1,x2) & or(x2,x3,x4) & skill:n(x3) & great:a(x3) & mastery:n(x4)

• Roll and turn skillfully

• and(e1,e2,e3) & roll:v(e2,x1,x2) & turn:v(e3,x1,x2) & skillfully:r(e1)

• An unintentional but embarrassing blunder

• blunder:n(x1) & but(x1,x2,x3) & unintentional:a(x2) & embarrassing:a(x3)

prepositions

• every preposition is a predicate with two arguments:
  • the first argument corresponding to the predicate of the head of the phrase, to which PP attaches
  • the second argument corresponds to prepositional object

examples:

• Deprive of value for payment

• deprive:v(e1,x1,x2) & of(e1,x3) & value:n(x3) & for(x3,x4) & payment:n(x4)

• Playing the position of pitcher on a baseball team

• playing:v(e1,x1,x2) & position:n(x2) & of(x2,x3) & pitcher:n(x3) & on(e1,x4) & baseball_team:n(x4)

complex nominals

• a new predicate nn is introduced to link together the collocating nouns.
• nn has a variable number of arguments, the first representing the result of aggregation of the nouns, the rest one for each noun

example:

• An organization created for business ventures
• organization:n(x2) & create(e1,x1,x2) & for(e1,x3) & nn(x3,x4,x5) & business:n(x4) & venture:n(x5)
• Government income credited to taxation
• nn(x2,x3,x4) & government:n(x3) & income:n(x4) & credit:v(e1,x1,x2) & to(e1,x5) & taxation:n(x5)

Examples

• A game played with rackets by two or four players who hit a ball back and forth over a net that divides a tennis court
• game:n(x2) & play:v(e1,x1,x2) & with(e1,x3) & racket:n(x3) & by(e1,x1) & or(x1,x4,x5) & two:n(x4) & four:n(x5) & player:n(x1) & hit:v(e2,x1,x6) & ball:n(x6) & back_and_forth:r(e2) & over(e2,x7) & net:n(x7) & divide:v(e3,x7,x8) & tennis_court:n(x8)