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General Course Program  -  Modules at the Universidade Nova de Lisboa (UNL)

Module	ECTS Credits	Person in Charge
Basic Modules
Advanced Logics	9	Reinhard Kahle
Foundations	12	Luis Moniz Pereira
Integrated Logic Systems	9	José Júlio Alferes
Logic and Constraint Programming	12	Pedro Barahona
Advanced Modules
Constraints	12	Pedro Barahona
Knowledge, Reasoning and Agents	12	Luis Moniz Pereira
Logic and Computation	12	Amilcar Sernadas
Semantic Web	12	Carlos Damasio

Description of the Advanced Modules

Knowledge, Reasoning and Agents

Other lecturers: José Júlio Alferes, João Alexandre Leite
This 12 ECTS advanced module is comprised of 3 equal-sized courses of 4 ECTS each:

• Course: Knowledge Representation
  Non-monotonic computational logic formalisms for declarative knowledge representation, including default logic, circumscription, and logic pro gramming. Temporal knowledge and action representation, including situation and event calculus. Methodologies for representing knowledge with them. Illustrative applications. Implemented systems and tools.
• Course: Computational Reasoning
  Computational logic forms of reasoning and their combination, including hypothetical, abductive, paraconsistent, belief revision, argumentative , counterfactual, debugging, updating, and prefering. Logic programming based semantics, procedures, and implementations. Illustrative applic ations. Implemented systems and tools.
• Course: Agents
  Computational logic paradigms and formalisms for expressing agents and agent societies, with emphasis on a Logic Programming approach. Agent and agent society architecture and evolution. Combining rationality and reactivity. Centralized and distributed control. Communication and cooperation among agents. Illustrative applications. Implemented systems and tools.

Person in charge:  Luis Moniz Pereira

Constraints

Other lecturers: Francisco Azevedo, Jorge Cruz, João Moura Pires
The module consists of 4 courses depicted below and of 3 ECTS each.

• Course: Topics in Finite Domain Constraints
  Lecturer: Pedro Barahona
  Consistency criteria for constraint networks: arc-, path-, and k-consistency. Algorithms to enforce these criteria, and study of their comp lexity. Implementation of constraint solvers: indexical constraints. Constructive approach for combining constraints. Constructive disjunction, and cardinality constraints. Global constraints: their specification and implementation. Redundant constraints: advantages and disadvanta ges of their use in schedulling, planning and other resource management applications.
• Course: Constraints over Sets and Optimisation
  Lecturer: Francisco Azevedo
  Representation of sets and multisets. Set variables and set features (maximum, minimum and cardinality). Operations on sets (set union, intersection, difference, disjointness, complement), related constraints and their propagation. Sets of sets: representation with union functi ons. Set constraint solvers: Conjunto and Cardinal. Applications: Set covering and partitioning, timetabling, digital circuits. Comparison wi th SAT. Optimisation. Branch and bound and local search.
• Course: Constraints on Continuous Domains
  Lecturer: Jorge Cruz
  Representation of continuous domains (intervals, boxes) and basic operations. Interval analysis: interval arithmetic, interval extensions of real functions and the interval Newton method. Constraint propagation: narrowing functions and constraint projections. Constraint decompositio n method and Newton constraint method. Consistency criteria for continuous domains: local consistency (interval, hull and box) and highe r order consistency (3B, bound and global hull). Introduction to differential equations..
• Course: Fuzzy Constraints
  Lecturer: João Moura Pires
  Introduction to fuzzy sets theory and to Possibility Theory. Generalization of CSP to FCSP. Fuzzy constraints and their dual interpretation. Min-FCSP. Constraint propagation in min-FCSP. Solving min-FCSP. Refining min-FCSP by discrimin and leximin-FCSP. Complexity issues. V(alued) -CSP and S(emiring)-CSP as general frameworks. Special cases of these general frameworks (Min-FCSP, Sigma-CSP, Max-CSP and Lexicographic CSP); their complexity.

Person in charge:  Pedro Barahona

Logic and Computation

Other lecturers: Narciso Garcia, Cristina Sernadas.
The module consists of two courses depicted below and of 6 ECTS each.

• Course: Computability Theory
  Semester:  Winter.
  Professor:  Narciso Garcia.
  Aims:  Develop the theory of recursive functions for establishing the mathematical foundations of the theory of computation. G\"odel's incompleteness theorem as an application.
  Syllabus:
  • Computability: Register machines. Descriptions. Recursive functions. Fundamental theorems of computability. Arithm etical hierarchy. Turing machines. Other approaches to recursive functions. Church's thesis. Hilbert's tenth problem. Cl assification of recursive functions.
  • Logic and computability: First-order arithmetic. Representability of recursive functions. Gödel's incompleteness theorem.
  Reading list:
  • J. Bell and M. Machover. A Course in Mathematical Logic. North-Holland, 1977.
  Assessment:  Homework assignments and final exam
• Course: Complements of Modal Logic
  Semester:  Spring.
  Professor:  Cristina Sernadas..
  Aims:  Develop the algebraic theory of modal logics.
  Syllabus: 
  • Preliminaries: algebra, logic and deduction.
  • Fundamentals: propositional modal languages; algebraic semantics; Kripke semantics; decidability and finite model property; Lindenbaum-Tars ki construction; local and global completeness; lattices of (quasi) normal modal logics; interpolation and Beth theorems. Universal algeb ra and duality: varieties; Stone representation; algebraic characterization of interpolation. Polymodal logics: fusion; fibring; preserva tion results. Quantified modal logics: topos semantics; local and global completeness.
  Reading list:
  • M. Kracht. Tools and Techniques in Modal Logic. Elsevier, 1999.
  • J. Bell. Toposes and Local Set Theories.Oxford University Press, 1988.
  • P. Blackburn, M. de Rijke and Y. Venema. Modal Logic. Cambridge University Press, 2001.
  • A. Chagrov and M. Zakharyaschev. Modal Logic. Oxford University Press, 1997.
  • G. E. Hughes and M. J. Cresswell. A New Introduction to Modal Logic. Routledge, 1996.
  • V. V. Rybakov. Admissibility of Logical Inference Rules. Elsevier, 1997.
  Assessment:  Homework assignments and final exam.

Person in charge:  Amilcar Sernadas

Semantic Web

Other Lecturers: Joaquim Nunes Aparício
This module covers both theoretical, technological and practical aspects of the development of Web-aware advanced information systems, in particular fo r the Semantic Web. The module is comprised of two courses of 6 ECTS each during two semesters, one covering XML technology and the other addressing K nowledge Representation for the Semantic Web.

• Course:
  The first part of the module describes XML based technology fo representing hierarchical and semi-structured data, and related W3Crecommendations: XML Schemas, XML Namespaces, and XML Base. The text-centered and data-centered documents views are discussed andcompared. XML data model integrity supporting mechanisms are analysed, namely XLink, XPointer and XML Inclusions. Querying and transformation languages for XML documents are described and deeply studied, in particular XSL based-languages (XPath and XSLT) and the more recent XQuery. The course continues by relating the database relational model (DBMSs) with the hierarchical model (XML), and studying the mappings between them. The course continues by presenting client-server architectures integrating XML and relational databases, as well as XML support in the major DBMSs. The course concludes with DOM and SAX programming techniques, and construction of Web Services using SOAP.
• Course:
  The second course, starts by explaining and motivating the origins of the Semantic Web and its logical layered structure. Some basic concepts are overviewed, namely UNICODE, URIs and IRIs, XML Base, XML Namespaces, XSL, and XML Canonicalization. The Resource Description Framework (RDF) and RDF Schema languages are introduced for describing resources and basic vocabularies in the Semantic Web. RDF(S) model theory and inference mechanisms are also addressed, as well as practical applications and its limitations. Description Logics are then introduced as a better knowledge representation formalism. Its constructs and semantics are introduced, as well the basic reasoning tasks and corresponding algorithms. The OWL language is presented and applications are provided. The course finishes, by studying the existing proposals for the integration of ontologies with rules in the Semantic Web, in particular the RuleML language proposal is discussed.

Person in charge:  Carlos Damasio

For further information, see the pages of the Mestrado em Lógica Computacional or contact Prof. Luis Moniz Pereira.