Introduction to formal semantics -

Transcription

1 Introduction to formal semantics - Introduction to formal semantics 1 / 25

2 structure Motivation - Philosophy paradox antinomy division in object und Meta language Semiotics syntax semantics Pragmatics Formal semantics in Computer Science Introduction to formal semantics 2 / 25

3 Motivation - Philosophy Problem of truth is sentence or statement true? I, we, now different meaning in different situations investigate only statements (intuitive) TARSKI scheme: X is true if and only if p name of p statement definition of the true predicate in S colloquial language Introduction to formal semantics 3 / 25

4 paradox Paradox definition A suicide murderer kills all that do not kill themselves. Paradox act commandment Give somebody a shed of paper with please turn around on both sites. No logical problems Introduction to formal semantics 4 / 25

5 antinomy Logical paradox or antinomy A suicide murderer kills all that do not kill themselves. if there is a prove that such person exists Antinomy by TARSKI ( X is true if and only if p ) This statement is not true. Introduction to formal semantics 5 / 25

6 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 Introduction to formal semantics 6 / 25

7 division in object und meta language To solve antinomies divide natural language Object language: to describe anything ( true, false, ) Order one Meta language: Object language + true, false Order two The sun is shining today. The statement above is true. The second statement here is true. Order one Order two Order three Introduction to formal semantics 7 / 25

8 division in object und meta language To solve antinomies divide natural language The statement The statement of order on one slide on 8 slide is not 8 true. is not true. There is a statement of order one on slide 8 that is false. Introduction to formal semantics 8 / 25

9 structure Motivation - Philosophy paradox antinomy division in object und meta language X is true if and only if p This The statement color is is late. not true. Semiotics syntax semantics pragmatics Formal semantics in Computer Science Introduction to formal semantics 9 / 25

10 Semiotics The study of signs and symbols Study of how meaning is constructed and understood Can be empirical or pure historical languages artificial languages syntax semantics pragmatics Introduction to formal semantics 10 / 25

11 syntax historical languages Study of the rules, or patterned relations The color is late. subject verb adjective Introduction to formal semantics 11 / 25

12 semantics historical languages Study of the aspects of meaning the relation that a sign has to other signs sense The color is late. the relation that a sign has to objects and objective situations, actual or possible reference Introduction to formal semantics 12 / 25

13 semantics historical languages Semantic levels: each word (lexical semantics) relationship between words (structural semantics) combination of sentences texts of different persons (dialog) Connection between semantic levels: MEANING(the color is late) = f(meaning(the), MEANING(color), MEANING(is), MEANING(late)) Frege principle Introduction to formal semantics 13 / 25

14 pragmatics historical languages Considers the environment Sentence meaning speaker's meaning Interested in sentences Empirical factors: Psychological activity by speaker Historical identifiable language habit Introduction to formal semantics 14 / 25

15 Semiotics The study of signs and symbols Study of how meaning is constructed and understood Can be empirical or pure historical languages syntax semantics pragmatics artificial languages syntax semantics pragmatics Introduction to formal semantics 15 / 25

16 syntax artificial languages 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 Introduction to formal semantics 16 / 25

17 semantics artificial languages defines a mathematical model describes the possible computations three major classes: Denotational semantics Operational semantics Axiomatic semantics Introduction to formal semantics 17 / 25

18 pragmatics artificial languages defines the behavior in environments Compiler OS Machine Introduction to formal semantics 18 / 25

19 structure Motivation - Philosophy paradox antinomy division in object und meta language X is true if and only if p The color is late. Semiotics syntax semantics pragmatics (empirical + pure ) Formal semantics in Computer Science Introduction to formal semantics 19 / 25

20 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 Introduction to formal semantics 20 / 25

21 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) Introduction to formal semantics 21 / 25

22 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 Introduction to formal semantics 22 / 25

23 Formal semantics in CS mathematical model of programming language by Static semantics properties that cannot change during execution Dynamic semantics properties that may change Var a : boolean; integer; If a THEN ELSE Introduction to formal semantics 23 / 25

24 Conclusion Motivation - Philosophy paradox antinomy division in object und Meta language X is true if and only if p The color is late. Semiotics syntax semantics Pragmatics (empirical + pure ) Formal semantics in Computer Science Introduction to formal semantics 24 / 25

25 Conclusion Questions? Introduction to formal semantics 25 / 25