Digital Repository

# A System for Models of First Order Theories

## DSpace/Manakin Repository

 dc.contributor.author AbdalBari, Anwar dc.date.accessioned 2012-10-12T14:24:41Z dc.date.available 2012-10-12T14:24:41Z dc.date.issued 2012-10-12 dc.identifier.uri http://hdl.handle.net/10464/4126 dc.description.abstract If you want to know whether a property is true or not in a specific algebraic structure, en_US you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language .( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders. dc.subject First order theories en_US dc.subject Computer programming. en_US dc.title A System for Models of First Order Theories en_US dc.degree.name M.Sc. Computer Science en_US dc.degree.level Masters en_US dc.contributor.department Department of Computer Science en_US dc.degree.discipline Faculty of Mathematics and Science en_US dc.embargo.terms None en_US
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