Logik für Informatiker Logic for computer scientists
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1 Logik für Informatiker for computer scientists WiSe 2011/12
2 Overview Motivation Why is logic needed in computer science? The LPL book and software Scheinkriterien
3 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
4 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
5 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
6 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
7 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
8 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
9 Why is logic needed in computer science? formal specification and verification databases, WWW, artificial intelligence algorithms & complexity metatheory (semi-)automated theorem proving programming languages
10 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
11 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
12 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
13 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
14 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
15 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
16 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
17 Formal specification and verification formal software and hardware development verification of existing software and hardware generation of test cases protocol verification, security (modal and temporal logics) properties of telephone systems Example: Pentium 4 arithmetic completely specified and verified with higher-order logic! Example: NASA uses logic for testing software
18 databases, WWW, artificial intelligence queries for web search; database queries (SQL) ontologies and semantic web expert systems linguistics Example: CYC is a very large knowledge base containing over 1.5 Million facts, rules-of-thumb and heuristics for reasoning about the objects and events of everyday life the CYC inference engine uses first-order logic!
19 databases, WWW, artificial intelligence queries for web search; database queries (SQL) ontologies and semantic web expert systems linguistics Example: CYC is a very large knowledge base containing over 1.5 Million facts, rules-of-thumb and heuristics for reasoning about the objects and events of everyday life the CYC inference engine uses first-order logic!
20 databases, WWW, artificial intelligence queries for web search; database queries (SQL) ontologies and semantic web expert systems linguistics Example: CYC is a very large knowledge base containing over 1.5 Million facts, rules-of-thumb and heuristics for reasoning about the objects and events of everyday life the CYC inference engine uses first-order logic!
21 databases, WWW, artificial intelligence queries for web search; database queries (SQL) ontologies and semantic web expert systems linguistics Example: CYC is a very large knowledge base containing over 1.5 Million facts, rules-of-thumb and heuristics for reasoning about the objects and events of everyday life the CYC inference engine uses first-order logic!
22 databases, WWW, artificial intelligence queries for web search; database queries (SQL) ontologies and semantic web expert systems linguistics Example: CYC is a very large knowledge base containing over 1.5 Million facts, rules-of-thumb and heuristics for reasoning about the objects and events of everyday life the CYC inference engine uses first-order logic!
23 databases, WWW, artificial intelligence queries for web search; database queries (SQL) ontologies and semantic web expert systems linguistics Example: CYC is a very large knowledge base containing over 1.5 Million facts, rules-of-thumb and heuristics for reasoning about the objects and events of everyday life the CYC inference engine uses first-order logic!
24 Algorithms & complexity if a graph property can be stated in monadic second-order logic, there is an efficient algorithm for it complexity classes can be characterized by classes of logical formulas Example: the proof of NL=Co-NL was based on this the hope is to push this further towards P=?NP
25 Algorithms & complexity if a graph property can be stated in monadic second-order logic, there is an efficient algorithm for it complexity classes can be characterized by classes of logical formulas Example: the proof of NL=Co-NL was based on this the hope is to push this further towards P=?NP
26 Algorithms & complexity if a graph property can be stated in monadic second-order logic, there is an efficient algorithm for it complexity classes can be characterized by classes of logical formulas Example: the proof of NL=Co-NL was based on this the hope is to push this further towards P=?NP
27 Algorithms & complexity if a graph property can be stated in monadic second-order logic, there is an efficient algorithm for it complexity classes can be characterized by classes of logical formulas Example: the proof of NL=Co-NL was based on this the hope is to push this further towards P=?NP
28 Metatheory Motivation set theory has been formalized in first-order logic this serves as a foundations for all of mathematics and theoretical computer science Gödel s completeness theorem for first-order logic: semantics can be captured by formal proofs even by machine-driven proofs! Gödel s incompleteness theorem for first-order logic + induction: some essential pieces of mathematics and theoretical computer science cannot be captured by formal systems!
29 Metatheory Motivation set theory has been formalized in first-order logic this serves as a foundations for all of mathematics and theoretical computer science Gödel s completeness theorem for first-order logic: semantics can be captured by formal proofs even by machine-driven proofs! Gödel s incompleteness theorem for first-order logic + induction: some essential pieces of mathematics and theoretical computer science cannot be captured by formal systems!
30 Metatheory Motivation set theory has been formalized in first-order logic this serves as a foundations for all of mathematics and theoretical computer science Gödel s completeness theorem for first-order logic: semantics can be captured by formal proofs even by machine-driven proofs! Gödel s incompleteness theorem for first-order logic + induction: some essential pieces of mathematics and theoretical computer science cannot be captured by formal systems!
31 Metatheory Motivation set theory has been formalized in first-order logic this serves as a foundations for all of mathematics and theoretical computer science Gödel s completeness theorem for first-order logic: semantics can be captured by formal proofs even by machine-driven proofs! Gödel s incompleteness theorem for first-order logic + induction: some essential pieces of mathematics and theoretical computer science cannot be captured by formal systems!
32 (Semi-)automated theorem proving logical properties of finite state machines can be automatically checked (model checkers) more complex systems need semi-automated proving verification of proofs is easy and fully automatic Example: some theorem about Boolean algebras has been found by a computer Example: several math text books have been verified with a semi-automatic prover (and small but inessential errors have been found)
33 (Semi-)automated theorem proving logical properties of finite state machines can be automatically checked (model checkers) more complex systems need semi-automated proving verification of proofs is easy and fully automatic Example: some theorem about Boolean algebras has been found by a computer Example: several math text books have been verified with a semi-automatic prover (and small but inessential errors have been found)
34 (Semi-)automated theorem proving logical properties of finite state machines can be automatically checked (model checkers) more complex systems need semi-automated proving verification of proofs is easy and fully automatic Example: some theorem about Boolean algebras has been found by a computer Example: several math text books have been verified with a semi-automatic prover (and small but inessential errors have been found)
35 (Semi-)automated theorem proving logical properties of finite state machines can be automatically checked (model checkers) more complex systems need semi-automated proving verification of proofs is easy and fully automatic Example: some theorem about Boolean algebras has been found by a computer Example: several math text books have been verified with a semi-automatic prover (and small but inessential errors have been found)
36 (Semi-)automated theorem proving logical properties of finite state machines can be automatically checked (model checkers) more complex systems need semi-automated proving verification of proofs is easy and fully automatic Example: some theorem about Boolean algebras has been found by a computer Example: several math text books have been verified with a semi-automatic prover (and small but inessential errors have been found)
37 (Semi-)automated theorem proving logical properties of finite state machines can be automatically checked (model checkers) more complex systems need semi-automated proving verification of proofs is easy and fully automatic Example: some theorem about Boolean algebras has been found by a computer Example: several math text books have been verified with a semi-automatic prover (and small but inessential errors have been found)
38 Programming languages Many programming languages use logical and, or, not Prolog = programming in logic concentrates on what instead of how involves non-deterministic search used for applications in linguistics and artificial intelligence
39 Programming languages Many programming languages use logical and, or, not Prolog = programming in logic concentrates on what instead of how involves non-deterministic search used for applications in linguistics and artificial intelligence
40 Programming languages Many programming languages use logical and, or, not Prolog = programming in logic concentrates on what instead of how involves non-deterministic search used for applications in linguistics and artificial intelligence
41 Programming languages Many programming languages use logical and, or, not Prolog = programming in logic concentrates on what instead of how involves non-deterministic search used for applications in linguistics and artificial intelligence
42 Programming languages Many programming languages use logical and, or, not Prolog = programming in logic concentrates on what instead of how involves non-deterministic search used for applications in linguistics and artificial intelligence
43 Programming languages Many programming languages use logical and, or, not Prolog = programming in logic concentrates on what instead of how involves non-deterministic search used for applications in linguistics and artificial intelligence
44 Landscape of logics Temporal logic Prop ModalProp of programs FOL ModalFOL Spatial logic HOL
45 propositional consequence Hintikka games propositional proofs resolution (semi-)automatic proving: SPASS, Isabelle first-order quantifiers first-order consequence
46 LPL book detailed introduction into first-order logic with many exercises Boole construct truth tables Tarski s world evaluate logical formulas within a blocks world Fitch construct proofs Grinder gives automatic feedback to your solutions requires purchase of the CD (ca. 13 EUR) or the book (ca. 25 EUR, with CD)
47 LPL book detailed introduction into first-order logic with many exercises Boole construct truth tables Tarski s world evaluate logical formulas within a blocks world Fitch construct proofs Grinder gives automatic feedback to your solutions requires purchase of the CD (ca. 13 EUR) or the book (ca. 25 EUR, with CD)
48 Rooms Motivation Tuesday 14:00-16:00 MZH 1400 Thursday 16:00-18:00 MZH 1470 Exercises (bring your Laptops with you!) within the course No lecture on Thursday, November 11 Web: ws11-12/logik/
49 Course Criteria successful solution of 10 exercises from 7 different chapters, with deadlines as given in the course to be found in the LPL book but: only those listed on the website, marked with grades grade is average of 10 best solutions, but only as good as the best fitch solution groups of 1-3 students (10/20/30 exercises, same grade for all) submitted to the Grinder or to me (depending on the exercise) and: presentation of solutions to the class, or oral exam ( Fachgespräch )
50 for working with the Grinder, each student/group needs an own new CD important: register at logic.informatik.uni-bremen.de under the same as for the Grinder try easy exercises first, to reach the minimum of 10 (later on, you can improve: only the 10 best solutions count) only exercises with a successful report (by the Grinder or us) count the Grinder is always right (but some old versions of Fitch are buggy)
The Formal Semantics of Programming Languages An Introduction. Glynn Winskel. The MIT Press Cambridge, Massachusetts London, England
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