Edward Hermann Haeusler

Referee assignment in sports leagues

Optimization in sports is a field of increasing interest. Combinatorial optimization techniques have been applied, for example, to game scheduling and playoff elimination. A common problem usually found in sports management is the assignment of referees to games already scheduled. There are a number of rules and objectives that should be taken into account when referees are assigned to games. We address a simplified version of a referee assignment problem common to many amateur leagues of sports such as soccer, baseball, and basketball. The problem is formulated by integer programming and its decision version is proved to be NP-complete. To tackle real-life large instances of the referee assignment problem, we propose a three-phase heuristic approach based on a constructive procedure, a repair heuristic to make solutions feasible, and a local search heuristic to improve feasible solutions. Numerical results on realistic instances are presented and discussed.

Maude Action Tool: Using Reflection to Map Action Semantics to Rewriting Logic

Action semantics (AS) is a framework for specifying the semantics of programming languages, in a very modular and readable way. Recently, the operational semantics of action notation (action semanticss specification language) has been rewritten using Modular SOS (MSOS), a new modular approach for specifying operational semantics. The new modular specification of action notation facilitates the creation of extensions to action semantics, to deal with new concepts, such as components. The Maude Action Tool uses the reflective capabilities of rewriting logic, implemented on the Maude system, to create an executable environment for action semantics and its potential extensions. This is achieved by a mapping between the MSOS and rewriting logic formalisms which, when applied to the MSOS semantics of each facet of action notation, yields a corresponding rewrite theory. Such rewrite theories are executed on action programs, that is, on the action notation translation of a given program P in a language L, according to Ls action semantics.

Ontology and Context

This paper considers a formal framework to contextualize ontologies and presents a formal algebra to manipulate these entities providing several ways of composing ontologies, contexts or both. The algebra gives the flexibility that is required to model applications where the meaning of an entity depends on environment constraints or where dynamic changes in the environment must be considered.

A Formal Approach to Real-Time Object Oriented Software

Abstract The ARTS paradigm involves a friendly user plane, where object oriented designs take place, and a corresponding formal plane where user decisions are verified, and which allows for early prototyping. The approach adopted for modelling real-time aspects (timed transition systems for the object’s life-cycle specification) relies on an extension of Henzinger’s Timed Transition Systems and Chang’s Metric Temporal Logic with δ-operators in the style of Segerberg, and actions modelling methods and message passing.

Propositional dynamic logic for Petri nets

Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyse concurrent programs with a very nice graphical representation. In this work, we propose a PDL to reasoning about Petri Nets. First we define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Finally, we present an axiomatization and prove completeness w.r.t. our semantics. The advantage of our approach is that we can do reasoning about Petri Nets using our dynamic logic and we do not need to to translate it to other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.

A Formal Framework for Modeling Context-Aware Behavior in Ubiquitous Computing

A formal framework to contextualize ontologies, proposed in [3], provides several ways of composing ontologies, contexts or both. The proposed algebra can be used to model applications in which the meaning of an entity depends on environment constraints or where dynamic changes in the environment have to be considered. In this article we use this algebra to formalize the problem of interpreting context information in ubiquitous systems, based on a concrete scenario. The main goal is to verify, on one hand, how the formal approach can contribute with a better understanding of the fundamental concepts of ubiquitous computing and, on the other hand, if this formal framework is flexible and rich enough to adequately express specific characteristics of the concrete application domain and scenario.

Using ontologies to formalize services specifications in multi-agent systems

One key issue in multi-agent systems (MAS) is their ability to interact and exchange information autonomously across applications. To secure agent interoperability, designers must rely on a communication protocol that allows software agents to exchange meaningful information. In this paper we propose using ontologies as such communication protocol. Ontologies capture the semantics of the operations and services provided by agents, allowing interoperability and information exchange in a MAS. Ontologies are a formal, machine processable, representation that allows to capture the semantics of a domain and, to derive meaningful information by way of logical inference. In our proposal we use a formal knowledge representation language (OWL) that translates into Description Logics (a subset of first order logic), thus eliminating ambiguities and providing a solid base for machine based inference.The main contribution of this approach is to make the requirements explicit, centralize the specification in a single document (the ontology itself), at the same that it provides a formal, unambigous representation that can be processed by automated inference machines.

Proof-graphs for Minimal Implicational Logic.

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study how to reduce the weight of propositional deductions. We present the formalism of proof-graphs for purely implicational logic, which are graphs of a specific shape that are intended to capture the logical structure of a deduction. The advantage of this formalism is that formulas can be shared in the reduced proof. In the present paper we give a precise definition of proof-graphs for the minimal implicational logic, together with a normalization procedure for these proof-graphs. In contrast to standard tree-like formalisms, our normalization does not increase the number of nodes, when applied to the corresponding minimal proof-graph representations.

Specifying ubiquitous systems through the algebra of contextualized ontologies

In this paper we present the algebra of contextualized ontologies and an approach to specify context-aware systems. The algebra is designed to support context moddeling and aims at the specification of modular and scalable description of arbitrarily complex systems. It takes contextualization as a basic notion and proposes a small set of simple and powerful operations to compose and decompose contextualized entities. The specification approach considers the gap between the formal specification and the real application and split the specification process in three levels variyng from the system design to the complete formalization using the algebra.

Using the Internal Logic of a Topos to Model Search Spaces for Problems

We present a structural model for (meta)heuristic search strategies for solving computational problems. The model is defined through the use of topos-theoretical tools and techniques, which provide an appropriate internal logic (with the language of local set theory) where objects of interest can be represented.