Introduction to formal semantics - Enrico Leonhardt Introduction - - PowerPoint PPT Presentation

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Introduction to formal semantics - Enrico Leonhardt Introduction - - PowerPoint PPT Presentation

Nov 01, 2023 442 likes •716 views

Introduction to formal semantics - Enrico Leonhardt Introduction to formal semantics 1 / 25 Enrico Leonhardt | Motivation | Semiotics | Formal semantics in CS | structure Motivation - Philosophy paradox antinomy

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Introduction to formal semantics 1 / 25

Enrico Leonhardt

Introduction to formal semantics

  • Enrico Leonhardt
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Introduction to formal semantics 2 / 25

Enrico Leonhardt

structure

  • Motivation - Philosophy

– paradox – antinomy – division in object und Meta language

  • Semiotics

– syntax – semantics – Pragmatics

  • Formal semantics in Computer Science

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 3 / 25

Enrico Leonhardt

Motivation - Philosophy

  • Problem of truth

– is sentence or statement true? – (intuitive) TARSKI scheme: “X is true if and only if p” – definition of the ‘true’ predicate in S

“I”, “we”, “now”…  different meaning in different situations  investigate only statements name of p statement

colloquial language

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 4 / 25

Enrico Leonhardt

paradox

  • Paradox definition
  • Paradox act commandment

 No logical problems

A suicide murderer kills all that do not kill themselves. Give somebody a shed of paper with “please turn around” on both sites.

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 5 / 25

Enrico Leonhardt

antinomy

  • Logical paradox or antinomy

 if there is a prove that such person exists

  • Antinomy by TARSKI (“X is true if and only if p” )

A suicide murderer kills all that do not kill themselves. This statement is not true.

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 6 / 25

Enrico Leonhardt

antinomy

  • Conditions to create an antinomy

1. Language is semantically closed

– statements in the language can contain its own ‘true’ predicate

2. Basic laws of logic

| Motivation | Semiotics | Formal semantics in CS |

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Enrico Leonhardt

division in object und meta language

  • To solve antinomies divide natural language

Object language: to describe anything (‘true’, ‘false’,…)

Meta language: Object language + ‘true’, ‘false’…

Order one Order two… The sun is shining today. The statement above is true. The second statement here is true.

Order one Order two Order three | Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 8 / 25

Enrico Leonhardt

division in object und meta language

  • To solve antinomies divide natural language

The statement on slide 8 is not true. The statement of order one on slide 8 is not true. There is a statement of order one on slide 8 that is false.

| Motivation | Semiotics | Formal semantics in CS |

The statement of order one on slide 8 is not true.

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Introduction to formal semantics 9 / 25

Enrico Leonhardt

structure

  • Motivation - Philosophy

– paradox – antinomy – division in object und meta language

  • Semiotics

– syntax – semantics – pragmatics

  • Formal semantics in Computer Science

“X is true if and only if p” | Motivation | Semiotics | Formal semantics in CS | This statement is not true. The color is late.

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Introduction to formal semantics 10 / 25

Enrico Leonhardt

Semiotics

  • The study of signs and symbols
  • Study of how meaning is constructed and understood
  • Can be empirical or ‘pure’

– syntax – semantics – pragmatics

historical languages artificial languages

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 11 / 25

Enrico Leonhardt

syntax

  • Study of the rules, or “patterned relations”

historical languages

The color is late. subject verb adjective

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 12 / 25

Enrico Leonhardt

semantics

  • Study of the aspects of meaning
  • the relation that a sign has to other signs  sense
  • the relation that a sign has to objects and
  • bjective situations, actual or possible  reference

historical languages

| Motivation | Semiotics | Formal semantics in CS |

The color is late.

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Introduction to formal semantics 13 / 25

Enrico Leonhardt

semantics

  • Semantic levels:

– each word (lexical semantics) – relationship between words (structural semantics) – combination of sentences – texts of different persons (dialog)

  • Connection between semantic levels:

historical languages

MEANING(the color is late)

= f(MEANING(the), MEANING(color), MEANING(is), MEANING(late))

Frege principle | Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 14 / 25

Enrico Leonhardt

pragmatics

  • Considers the environment
  • Sentence meaning  speaker's meaning
  • Interested in sentences
  • Empirical factors:

– Psychological activity by speaker – Historical identifiable language habit

historical languages

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 15 / 25

Enrico Leonhardt

Semiotics

  • The study of signs and symbols
  • Study of how meaning is constructed and understood
  • Can be empirical or ‘pure’

– syntax – semantics – pragmatics

historical languages artificial languages

| Motivation | Semiotics | Formal semantics in CS |

– syntax – semantics – pragmatics

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Introduction to formal semantics 16 / 25

Enrico Leonhardt

syntax

  • defines a formal grammar, or simply grammar
  • sets of rules for how strings in a language can be

generated

  • rules for how a string can be analyzed to determine

whether it is a member of the language

artificial languages

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 17 / 25

Enrico Leonhardt

semantics

  • defines a mathematical model

– describes the possible computations – three major classes:

  • Denotational semantics
  • Operational semantics
  • Axiomatic semantics

artificial languages

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 18 / 25

Enrico Leonhardt

pragmatics

artificial languages

| Motivation | Semiotics | Formal semantics in CS |

  • defines the behavior in environments
  • Compiler
  • OS
  • Machine
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Introduction to formal semantics 19 / 25

Enrico Leonhardt

structure

  • Motivation - Philosophy

– paradox – antinomy – division in object und meta language

  • Semiotics

– syntax – semantics – pragmatics

  • Formal semantics in Computer Science

“X is true if and only if p”

(empirical + ‘pure’)

| Motivation | Semiotics | Formal semantics in CS | The color is late.

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Introduction to formal semantics 20 / 25

Enrico Leonhardt

Formal semantics in CS

  • mathematical model of programming language by
  • Denotational semantics

– each phrase in the language is translated into a denotation, i.e. a phrase in some other language

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 21 / 25

Enrico Leonhardt

Formal semantics in CS

  • mathematical model of programming language by
  • Denotational semantics

– each phrase in the language is translated into a denotation, i.e. a phrase in some other language

  • Operational semantics

– execution of the language is described directly (rather than by translation)

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 22 / 25

Enrico Leonhardt

Formal semantics in CS

  • mathematical model of programming language by
  • Denotational semantics

– each phrase in the language is translated into a denotation, i.e. a phrase in some other language

  • Operational semantics

– execution of the language is described directly (rather than by translation)

  • Axiomatic semantics

– rules of inferences to reason from meaning of input to meaning of output

| Motivation | Semiotics | Formal semantics in CS |

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Introduction to formal semantics 23 / 25

Enrico Leonhardt

Formal semantics in CS

  • mathematical model of programming language by
  • Static semantics

– properties that cannot change during execution

  • Dynamic semantics

– properties that may change

| Motivation | Semiotics | Formal semantics in CS |

Var a : integer; … If a THEN … ELSE … Var a : boolean; … If a THEN … ELSE …

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Introduction to formal semantics 24 / 25

Enrico Leonhardt

Conclusion

  • Motivation - Philosophy

– paradox – antinomy – division in object und Meta language

  • Semiotics

– syntax

– semantics

– Pragmatics

  • Formal semantics in Computer Science

| Motivation | Semiotics | Formal semantics in CS | “X is true if and only if p”

(empirical + ‘pure’)

The color is late.

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Introduction to formal semantics 25 / 25

Enrico Leonhardt

Conclusion

| Motivation | Semiotics | Formal semantics in CS |

Questions?