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Mathematical Logic for Computer Science

Mordechai (Moti) Ben-Ari

http://www.weizmann.ac.il/sci-tea/benari/


The repository contains programs implementing algorithms from my textbook Mathematical Logic for Computer Science, Springer, 2012, ISBN 978-1-4471-4128-0.

The programs are written in Prolog and were run using SWI Prolog.

Licence

Copyright 2002--2018 by Moti Ben-Ari under the GNU GPL license.

Materials

Documentation

The programs are documented in mlcs-programs-documentation.tex from which the pdf file was derived.

Directory sturcture

  • common - common modules and files used by other programs
  • prop - propositional calculus
  • bdd - binary decision diagrams
  • fol - first order logic
  • lp - logic programming
  • tl - temporal logic

For each program p.pro, there is a file p-t.pro which contains test programs. The programs use the predicate file_search_path to access the common modules in the common directory, so maintain the relative directory structure.

List of files:

Directory common:

  • ops.pro - declaration of operators with precedence and associativity.
  • def.pro - correspondance between symbols and internal operators. - semantic definition of Boolean operators.
  • intext.pro - conversion from external to internal format and conversely.
  • io.pro - display procedures for all programs (except BDDs).
  • cnfpro.pro - conversion of a formula to CNF

Directory prop: (propositional calculus)

  • tt.pro - truth tables.
  • tabl.pro - semantic tableaux.
  • systab.pro - systematic semantic tableaux. - note: tabl and systab share a test program tabl-t.pl.
  • check.pro - Hilbert proof checker.
  • resolv.pro - resolution.
  • bdd.pro - binary decision diagrams

Directory fol: first order logic

  • tabl.pro - semantic tableaux.
  • check.pro - Hilbert proof checker.
  • cnffol.pro - conver to CNF
  • skolem.pro - skolemize a formula.
  • unify.pro - unification algorithm.
  • resolv.pro - resolution.
  • utility.pro - procedures common to more than one file.

Directory tl: (temporal logic)

  • tl.pro - semantic tableaux .
  • peter.pro - state diagram for Peterson's algorithm.
  • sym.pro - symbolic model checking.

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