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 – division in object und Meta language • Semiotics – syntax – semantics – Pragmatics • Formal semantics in Computer Science Introduction to formal semantics 2 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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… Order one The sun is shining today. The statement above is true. Order two The second statement here is true. Order three Introduction to formal semantics 7 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | division in object und meta language • To solve antinomies divide natural language The statement of order one on slide 8 is not true. The statement of order one on slide 8 is not true. The statement on slide 8 is not true. There is a statement of order one on slide 8 that is false. Introduction to formal semantics 8 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | structure • Motivation - Philosophy “X is true if and only if p” – paradox – antinomy – division in object und meta language This statement is not true. The color is late. • Semiotics – syntax – semantics – pragmatics • Formal semantics in Computer Science Introduction to formal semantics 9 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | syntax historical languages • Study of the rules, or “patterned relations” The color is late. subject verb adjective Introduction to formal semantics 11 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 – syntax – semantics – semantics – pragmatics – pragmatics Introduction to formal semantics 15 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | pragmatics artificial languages • defines the behavior in environments • Compiler • OS • Machine Introduction to formal semantics 18 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | structure • Motivation - Philosophy “X is true if and only if p” – paradox – antinomy – division in object und meta language The color is late. • Semiotics (empirical + ‘pure’) – syntax – semantics – pragmatics • Formal semantics in Computer Science Introduction to formal semantics 19 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | 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 : integer; Var a : boolean; … … If a THEN If a THEN … … ELSE ELSE … … Introduction to formal semantics 23 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | Conclusion • Motivation - Philosophy “X is true if and only if p” – paradox – antinomy – division in object und Meta language The color is late. • Semiotics (empirical + ‘pure’) – syntax – semantics – Pragmatics • Formal semantics in Computer Science Introduction to formal semantics 24 / 25 Enrico Leonhardt
| Motivation | Semiotics | Formal semantics in CS | Conclusion Questions? Introduction to formal semantics 25 / 25 Enrico Leonhardt
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