Author | Suman Roy |
Title | Soundness and Completeness Results in Partially-interpreted Logics |
Thesis Supervisor | Vijaya Chandru |
Date of Defence | 6 November, 1998 |
Institute granting Degree | Indian Institute of Science, Bangalore |
Current Address | Email: suman@imsc.ernet.in |
The Institute of Mathematical Sciences, Chennai 600 113 |
Soundness and completeness show the equivalence of syntactic proof methods and the semantics of the logic and are therefore fundamental properties that we expect of any logic applied to problems in computer science.
The Constraint Logic Programming (CLP) scheme is a formal framework that extends traditional logic programming, on Horn clauses, in a natural way. Using functions and certain predicates (called constraints) interpreted in a pre-defined computational domains (e.g., reals, booleans, finite and infinite trees), CLP has been able to successfully model many practical problems. More importantly, the scheme provides an orchestration of highly efficient solvers from these interpreted domains in carrying out inference tasks. Negation as (finite) failure is a fundamental technique for implementing default reasoning in the context of logic programming. In part one of the thesis we give a resolution proof of the soundness and completeness of Negation as failure in the framework of CLP.
Real-time logics have been proposed in recent years to support the formal specification and formal verification of physical systems. An important aspect of these logics is their ability to model the temporal behaviour of such systems. This is facilitated in real-time logics by assuming ``time'' to belong to the domain of natural or real numbers and by assuming interpretations of function and predicate symbols (as in arithmetic). In part two of the thesis we investigate two real-time logics called ``Neighbourhood Logic'' (NL) and its extension ``Duration Calculus''. We also propose a sound and relatively complete proof system for Duration Calculus.