Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Logical analysis of natural language
Vojtěch Kovář
Natural Language Processing Centre
Faculty of Informatics, Masaryk University
Botanická 68a, 602 00 Brno
xkovar3@fi.muni.cz
PA153 Natural Language Processing
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Outline
1 Motivation
2 Predicate logic
3 What is meaning?
4 Transparent intensional logic
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Logical analysis of natural language
Sentence → logical formula
formal reasoning
interlingua for machine translation
precise expressions
Which formalism?
(first order) predicate logic
modal logics
intensional logics (IL, Richard Montague)
transparent intensional logic (TIL)
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Natural language → predicate logic
What are formulas for
„Some prime numbers are even”
„Some odd numbers are even”
„Some smart people are lazy”
„No bachelor is married”
„No bachelor is rich”
„Miloš Zeman is the president of CR.”
„Karel counts 5 + 7”
What is wrong?
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Natural language → predicate logic
What are formulas for
„Some prime numbers are even”
„Some odd numbers are even”
„Some smart people are lazy”
„No bachelor is married”
„No bachelor is rich”
„Miloš Zeman is the president of CR.”
„Karel counts 5 + 7”
What is wrong?
different types of truth
granularity of the description is insufficient
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Natural language → predicate logic
Karel counts 5 + 7
5 + 7 = 12
Karel counts 12
Miloš Zeman is the president of CR.
Karel Schwarzenberg wanted to become the president of CR.
Karel Schwarzenberg wanted to become Miloš Zeman.
It is not true that the king of France is bald-headed
The king of France has some hair on his head.
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Natural language → predicate logic
Predicate logic can be used for natural language analysis
some applications are doing it
but not in all cases
we need to be aware of the limits
work-arounds are possible but may be complicated
Advantages of predicate logic
it is simple
it is well explored
inference machine exists
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
What is the meaning of an expression?
Frege’s model of semantics
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Conception of possible worlds
A possible world
a set of non-contradictory formulas about the universe
the current world is one of the possible worlds
Empirical truth
the truth of a formula depends on the particular world
meaning is always world-independent
Intensional logics
intensions (world-independent)
extensions (denotates, objects in a particular world)
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Transparent intensional logic
Pavel Tichý, Pavel Materna
Procedural logic
possible worlds + possible times
meaning is a emphconstruction, i.e. abstact procedure
(algorithm) which takes the current world and time and
outputs the denotate (the particular object)
coded as lambda function
Typed logic
o – true, false
ι – set of individuums
τ – set of real numbers (or time moments)
ω – set of possible worlds
((oτ)ω) – proposition
(((oι)τ)ω) – property ((oι)τω)
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Transparent intensional logic – examples
Miloš Zeman je prezidentem CR.
λwλt[ = Miloš_Zeman President_CRwt ]
type oτω Miloš_Zeman/ι President_CR/ιτω = /(oιι)
Schwarzenberg wanted to become CR.
λwλt[ want_to_becomewt Schwarzenberg President_CR ]
oτω Schwarzenberg/ι President_CR/ιτω want_to_become/(oιιτω)
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Transparent intensional logic – examples
5 + 7
[ + 5 7 ]
type τ 5, 7/τ + /(τττ)
Karel counts 5 + 7.
λwλt[ countwt Karel 0[ + 5 7 ] ]
type oτω
0[+ 5 7]/∗1 count/(oι∗1)wt Karel/ι
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Normal translation algorithm
Automatic conversion of sentences into TIL constructions
doc. Aleš Horák
morphological analysis
syntactic analysis
conversion from tree to TIL formula
type check
output of all the layers is ambiguous
implementation within the Synt parser, currently
experiments with other parsers (SET)
Further requirements
lexicon of types (“snow” vs. “give” – exploitation of
valency lexicons)
rules for type control
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Transparent intensional logic – pros and cons
Advantages
correct and very precise analysis
makes general correct reasoning possible
Disadvantages
very abstract and complex
not really wide-spread
experts often do not agree on correct analysis
Vojtěch Kovář FI MU Brno
Logical analysis of natural language
Outline Motivation Predicate logic What is meaning? Transparent intensional logic
Transparentní intenzionální logika na FI
doc. Aleš Horák
prof. Marie Duží
subjects Introduction to Transparent Intensional Logic
Small corpus of correct constructions for Czech
https://corpora.fi.muni.cz/til
Semantic network of constructions
as a knowledge base for automatic reasoning
Vojtěch Kovář FI MU Brno
Logical analysis of natural language