Past, Present, and Infinite Future

I was supposed to deliver one of the speeches at Wolfgang Thomas\u27s retirement ceremony. Wolfgang had called me on the phone earlier and posed some questions about temporal logic, but I hadn\u27t had good answers at the time. What I decided to do at the ceremony was to take up the conversation again and show how it could have evolved if only I had put more effort into answering his questions. Here is the imaginary conversation with Wolfgang. The contributions are (1) the first direct translation from counter-free omega-automata into future temporal formulas, (2) a definition of bimachines for omega-words, (3) a translation from arbitrary temporal formulas (including both, future and past operators) into counter-free omega-bimachines, and (4) an automata-based proof of separation: every arbitrary temporal formula is equivalent to a boolean combination of pure future, present, and pure past formulas when interpreted in omega-words

A One-Pass Tree-Shaped Tableau for Defeasible LTL

Defeasible Linear Temporal Logic is a defeasible temporal formalism for representing and verifying exception-tolerant systems. It is based on Linear Temporal Logic (LTL) and builds on the preferential approach of Kraus et al. for non-monotonic reasoning, which allows us to formalize and reason with exceptions. In this paper, we tackle the satisfiability checking problem for defeasible LTL. One of the methods for satisfiability checking in LTL is the one-pass tree shaped analytic tableau proposed by Reynolds. We adapt his tableau to defeasible LTL by integrating the preferential semantics to the method. The novelty of this work is in showing how the preferential semantics works in a tableau method for defeasible linear temporal logic. We introduce a sound and complete tableau method for a fragment that can serve as the basis for further exploring tableau methods for this logic

On the Decidability of a Fragment of preferential LTL

Linear Temporal Logic (LTL) has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. Non-monotonic reasoning, on the other hand, allows us to formalize and reason with exceptions and the dynamics of information. The goal of this paper is therefore to enrich temporal formalisms with non-monotonic reasoning features. We do so by investigating a preferential semantics for defeasible LTL along the lines of that extensively studied by Kraus et al. in the propositional case and recently extended to modal and description logics. The main contribution of the paper is a decidability result for a meaningful fragment of preferential LTL that can serve as the basis for further exploration of defeasibility in temporal formalisms

Temporal and Contextual Dependencies in Relational Data Modeling

Although a solid theoretical foundation of relational data modeling has existed for decades, critical reassessment from temporal requirements’ perspective reveals shortcomings in its integrity constraints. We identify the need for this work by discussing how existing relational databases fail to ensure correctness of data when the data to be stored is time sensitive. The analysis presented in this work becomes particularly important in present times where, because of relational databases’ inadequacy to cater to all the requirements, new forms of database systems such as temporal databases, active databases, real time databases, and NoSQL (non-relational) databases have been introduced. In relational databases, temporal requirements have been dealt with either at application level using scripts or through manual assistance, but no attempts have been made to address them at design level. These requirements are the ones that need changing metadata as the time progresses, which remains unsupported by Relational Database Management System (RDBMS) to date. Starting with shortcomings of data, entity, and referential integrity in relational data modeling, we propose a new form of integrity that works at a more detailed level of granularity. We also present several important concepts including temporal dependency, contextual dependency, and cell level integrity. We then introduce cellular-constraints to implement the proposed integrity and dependencies, and also how they can be incorporated into the relational data model to enable RDBMS to handle temporal requirements in future. Overall, we provide a formal description to address the temporal requirements’ problem in relational data model, and design a framework for solving this problem. We have supplemented our proposition using examples, experiments and results

Certificates for decision problems in temporal logic using context-based tableaux and sequent calculi.

115 p.Esta tesis trata de resolver problemas de Satisfactibilidad y Model Checking, aportando certificados del resultado. En ella, se trabaja con tres lógicas temporales: Propositional Linear Temporal Logic (PLTL), Computation Tree Logic (CTL) y Extended Computation Tree Logic (ECTL). Primero se presenta el trabajo realizado sobre Certified Satisfiability. Ahí se muestra una adaptación del ya existente método dual de tableaux y secuentes basados en contexto para satisfactibilidad de fórmulas PLTL en Negation Normal Form. Se ha trabajado la generación de certificados en el caso en el que las fórmulas son insactisfactibles. Por último, se aporta una prueba de soundness del método. Segundo, se ha optimizado con Sat Solvers el método de Certified Satisfiability para el contexto de Certified Model Checking. Se aportan varios ejemplos de sistemas y propiedades. Tercero, se ha creado un nuevo método dual de tableaux y secuentes basados en contexto para realizar Certified Satisfiability para fórmulas CTL yECTL. Se presenta el método y un algoritmo que genera tanto el modelo en el caso de que las fórmulas son satisfactibles como la prueba en el caso en que no lo sean. Por último, se presenta una implementación del método para CTL y una experimentación comparando el método propuesto con otro método de similares características