MSc ACS: Data and Knowledge Management

Automated reasoning plays an important role in computer science because an incredible array of problems can be expressed as satisfiability tests or consequence queries. This means areas such as analyis, verification and security of software and hardware, knowledge engineering, AI and computational mathematics require support from automated reasoning tools. They are, for example, used in large software and hardware companies such as Microsoft and Intel for software and hardware analysis, synthesis and verification. An important part of systems development processes concerns reasoning about the behaviour of the systems in order to verify the correctness of the behaviour.  Also, in web and agent technologies automated reasoning methods are used for the intelligent processing of large ontologies, for decision making based on knowledge bases of structured data, and for formal specification and verification of web services. The motivation of the course is the introduction and study of a subset of the most important methods, techniques and tools used nowadays. These include SAT solvers, theory reasoners (SMT) and first-order reasoners.

The course aims at providing an understanding of the foundation of propositional logic, first-order logic and important theories for modelling and reasoning specifying properties of programs. It covers practical and theoretical techniques and results that form the basis of resolution reasoning systems and the DPLL reasoning algorithm, which is used in SAT and SMT solvers. Verification and automated analysis of security protocols are discussed as important application domains.  

On successful completion of this unit, a student should be able to:

• Model information in the language of propositional logic, first-order logic, and integrated theories relevant to software verification;
• Translate logical representations in English;
• Describe important notions such as soundness, refutational completeness, decidability;
• Explain relationships between satisfiability, unsatisfiability validity and equivalence (also relative to a theory), and exploit them for automated reasoning and verification;
• Check these using truth tables, resolution, the DPLL algorithm and the DPLL(T) algorithm;
• Describe and apply conjunctive and clausal normal form transformations;
• Determine how sets (clauses) compare using orderings, and determine maximal elements (literals);
• Find and determine interpretations for clauses (formulas), and compute candidate models;
• Apply the basic unification algorithm to unify terms and atomic formulas;
• Use orderings and selection refinements to restrict how inferences are performed in resolution;
• Simplify and determine redundancy of clauses;
• Use a first-order reasoner to establish properties of relations and analyse a security protocol;
• Use a SAT/SMT solver to verify properties of data structures;

The following lists the topics to be covered in the course. The teaching days will contain a mixture of lectures, examples classes, supervised laboratories and self-study. The number of lectures for each topic are given in brackets.

* Introduction (1)
* Orderings, multi-sets (1)
* Propositional reasoning
      + Language of propositional logic, semantics, truth tables (1)
      + Satisfiability, validity, equivalence, decidability (1)
      + Normal forms, CNF, clauses (1)
      + Propositional resolution, redundancy elimination (1)
      + DPLL and SAT-solving (1)
      + Logical modelling (1)
      + Using SAT/SMT solver (demo & lab)
* General first-order reasoning
      + Language of first-order logic, modelling (2)
      + substitution, semantics (1)
      + Normal forms, clauses (2)
      + Herbrand interpretations (1)
      + Soundness, literal & clause orderings, saturation (1)
      + Model construction (1)
      + Unication for general resolution (1)
      + Basic general resolution, ordering & selection refinements (2)
* Verification
      + Reasoning modulo theories (SMT): equality, data structures (2)
      + Verification, automated analysis of security protocols (2)
      + Using SPASS (demo & lab)

Lectures

Lecturers will be interspersed with example classes and labs on teaching days

Examples classes

Example classes will take place on teaching days

Laboratories

Labs will take place on teaching days

Exercise classes; assessment and feedback on written assignments.