Foundations of Semantic Technologies: Recommended reading
This page includes Web links and additional resources that student might
wish to read in addition to the lecture notes. The following
abbreviations are used below:
[EM] Elliot Mendelson "Introduction to Mathematical Logic", 4th edition,
published by Chapman & Hall, 1997.
[MBA] Mordechai BenAri
Mathematical Logic For Computer Science, corrected 3rd edition,
Springer 2008. Available in the library on reserve, for short term loan.
[RS] Raymond Smullyan ``FirstOrder Logic'', Dover Publications, 1995.
[SC] Stephen Cook
CSC 438F/2404F: Computability and Logic (University of Toronto),
Lecture Notes, Fall 2008.
[SS] Stephen Simpson
Lecture Notes on Mathematical Logic for MATH557.
MATH 557 is an introductory course on mathematical logic
at Penn State University (USA).
[TG] Timothy Gowers (Editor)
The Princeton Companion to Mathematics, Part 1 "Introduction",
Section I.2:
The Language and Grammar of Mathematics,
pages 816, Princeton University Press, 2008.

January 12, 2011:
Introduction and Overview. You might wish to
read
slides
prepared by Ian Horrocks and Alan Rector for the CS646 course (at
University of Manchester, UK) named
The Semantic Web: Ontologies and OWL. In addition, it might help to
read
these
slides prepared by Grigoris Antoniou and Frank van Harmelen for
Chapter 1 of their book
A Semantic Web Primer
(2nd edition, MIT Press, 2008: this book is available on reserve for
short term loan).
The W3C provides plenty of information about
Semantic
Web. Explore this Web page if you would like to learn more, but
this is not required.
Propositional logic:
You can find all definitions, theorems and many examples in
Stephen Simpson's lecture notes:
Read Chapter 1, pages 39. Also,
[SC]
Propositional calculus: pages 2 and 3 only.

January 19, 2011.
Propositional logic: [RS] Chapter 1 and [MBA] Chapter 2.
[SC]
Propositional calculus: pages 46 only. Also, in [SS], you can read
Chapter 1, pages 912. Semantic Tableau: construction. [MBA]: Chapter 2.

January 26, 2011.
Propositional Logic: Soundness and Completeness of semantic tableau.
[MBA]: Chapter 2. A brief summary is provided in S.Simpson's lecture notes
[SS]:
pages 1822. (Koenig's Lemma, Compactness).
You can also read [RS]: Chapters 2 and 3.
Inclass presentation: Introduction to XML, XML Schema and Namespaces.
Selected
Slides (a PDF file) are taken from the book
"A Semantic Web Primer". The purchase order example is available in
XML Schema Primer, Section 2.1
at the W3C Web pages.

February 2, 2011.
Introduction to first order logic (FOL). Basic Semantic Definition (BSD).
You can find an excellent introduction to FOL in [EM]: Sections 2.1 and 2.2.
Semantics of FOL: satisfiability, logical consequence, validity.
Logical equivalence: examples.
[SC]
Predicate Calculus, pages 1824.
You can also read S.Simpson's lecture notes
Sections 2.1, 2.2 and 2.4: pages 2530 and pages 3740.
Substitution in terms and in formulas, a term freely
substitutable for a variable in a formula, substitution theorem.
[SC]
Predicate Calculus, pages 25  27. You might wish to read also
Chapter 5 and
Chapter 6 (pages 2339) from Stefan Bilaniuk's
A Problem Course in
Mathematical Logic (LaTeX source is available too).
There are several related articles in Stanford Encyclopedia
of Philosophy, e.g., read
Section 4
on Semantics in the entry on classical logic (by Stewart Shapiro)
and
Section 1: Firstorder languages and structures in the entry
Firstorder Model Theory (by Wilfrid Hodges).

February 9, 2011.
Proofs in FOL. Semantic tableau: examples, Gammarules, Deltarules,
systematic construction of semantic tableau, soundness and completeness.
Godel completeness theorem for FOL. Read [MBA], Section 5.5.
Also, consult Dr. D.Delic's handouts
about semantic tableau that he prepared for his undegraduate Ryerson
course
MTH714 (Logic and Computability):
read Section 2.6 (tableau in propositional logic) and
read Section 5.5 (tableau in FOL); you may skip other sections.
Undecidability of the satisfiability problem for FOL formulas when
vocabulary includes at least one binary predicate in addition to
equality. Compactness of FOL. Finitely axiomatizable theories,
incomplete and complete theories, nonstandard models of theories.
[SC]
Lecture Notes: pages 49  52.

February 16, 2011.
Read in the textbook Chapter 2 (Simple Ontologies in RDF and RDF Schema)
and Sections 3.1 and 3.2.
Describing Web Resources in RDF: slides to Chapter 3 of the textbook
"Semantic Web Primer".
Michael Zakharyaschev's slides (slides 36  60) on RDF, RDF Schema
and RDF/S semantics prepared for his Semantic Web course at
University of London. Pascal Hitzler's slides
on RDF Schema and on
RDF Semantics. (The latter slides are prepared for the course
Knowledge Representation for the Semantic Web at Wright State
University, Ohio, USA.). Note that there is overlap between slides:
you can pay attention only to those slides which we covered in class.
The following links are optional: you are not required to read
documents at W3C linked here.
RDF and
RDF Schema.
In January 2011, W3C started a new
RDF Working Group
chartered to update the 2004 version of the Resource Description
Framework (RDF) Recommendation.

March 2, 2011. Introduction to Description Logics (DL).
Slides
(Part 1) of the tutotial
Description Logic: a Formal Foundation for Languages and Tools
presented by
Ian Horrocks.
Tutorial at the Semantic Technology Conference (SemTech) held in San
Francisco, California, USA, June 2227, 2010.
A readable introduction to DL is provided in
Sections 3.1, 3.2, 3.3.1 and 3.7 (pages 110 and 3133) from the Chapter 3
"Description Logics" written by F. Baader, I. Horrocks, and U. Sattler
and published in Handbook of Knowledge Representation,
pages 135179, Elsevier, 2007.
Read Sections 5.1.1 and 5.1.2 in the textbook (pages 159164).

March 16, 2011.
Semantics of Description Logics (DL). Read Section 5.2, pages 172180.
Reasoning in DLs.
Michael Zakharyaschev's slides on automated reasoning in DLs
(do exercises on slides 19 and 20). Reducing inference problems to the
(un)satisfiability problem. Negation Normal Form.
Tableaux Algorithm with blocking for ALC. Read the textbook
Sections 5.3  5.3.3 (pages 181196).
Pascal Hitzler's slides 440 on tableaux with blocking for ALC.
Also, read Michael Zakharyaschev's
slides 826 on tableaux in ALC (without blocking), but note that
notation is different from the textbook.
Exploring the following links is not required.
Section 3.4 (pages 1216) from the Chapter 3 on "Description Logics"
written by F. Baader, I. Horrocks, and U. Sattler.
Several important and influential papers on DLs are linked
from a course on
Description Logics taught by Enrico Franconi at Free University
of BozenBolzano, Italy. Some of these papers are included in the
comprehensive
Description Logic Handbook, a paperback copy of the 2nd edition,
published by Cambridge University Press, 2011.

March 23, 2011: OWL2 and its fragments.
OWL 2 Reference Card
is a handy summary of OWL2.
Read the textbook: Chapter 4 (pages 111156) and Section 5.1.35.2
(pages 165181).
The description logic SROIQ(D) provides logical foundations for OWL2.
The slides 1525 about the
description logic SROIQ are prepared by Pascal Hitzler for his
course
"Knowledge Representation for the Semantic Web". He also prepared
slides about
OWL syntax.
Ian Horrocks presented a tutorial on OWL2 to
Ontolog Forum on Thursday, July 29, 2010. Read his
slides and listen to an
audio recording of the session (you need MP3 compatible player to
listen).
The following links are optional: you are not required to read
W3C documents linked here.
Web Ontology Language (OWL2) Primer and more details about
fragments (profiles) of OWL2. Also, OWL2 has
Formal Direct Semantics
 Read the texbook, Chapter 6: Sections 6.1  6.3.
Ontologies and Rules. Datalog: syntax and semantics.
Combining rules with OWL DL. Rule Interchange Format (RIF).
Part 2: OWL2 Rules. Tutorial at the 32nd Annual German Conference on
Artificial Intelligence
(on September 15, 2009) prepared by
Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph.
This tutorial also includes
Part 1: Introduction to OWL 2 that covers OWL2.
The following links are optional: you are not required to read
W3C documents linked here.
RIF Primer and
RIF Overview.
RIF became W3C Recommendation on 22 June 2010.
 SPARQL. Conjunctive Queries for OWL DL. Chapter 7 of the textbook.
Foundations of Semantic Technologies