Jonathan Stillman

Tachyon: A constraint-based temporal reasoning model and its implementation

We provide an overview of Tachyon, an implementation of a constraint-based model for representing and reasoning about qualitative and quantitative aspects of time. Tachyons data model provides substantial expressiveness, fast computation over convex intervals, and will serve as a testbed for topology-driven techniques for handling calculations over non-convex intervals. Our implementation of this model features a graphical interface using X-Windows and InterViews. We are currently exploring the use of Tachyon in a number of areas, including scheduling, project planning, feasibility analysis, and spatio-temporal data management.

Temporal Reasoning for Automated Workflow in Health Care Enterprises

We have demonstrated through example clinical scenarios, and results with our temporal reasoner Tachyon that temporal reasoning can be a valuable tool for managing and improving the workflow of business processes, particularly in healthcare. We have also identified areas where Tachyon can be extended to provide even more support for automated workflow.

Hardware Verification in the Interactive VHDL Workstation

Formal Hardware Verification has gained a lot of attention recently as a viable alternative to simulation. Several notable achievements have been reported, such as Hunt [4], Birtwistle et. al. [1]. In this document we describe one aspect of an ongoing project aimed at developing an integrated environment for hardware description, simulation, and verification. We report here on the current efforts toward developing tools for formal verification of hardware and how these tools interact with other parts of the IVW workstation being developed at General Electric Research and Development Center (GE CRD). This is of necessity a preliminary document, as our work in developing an environment for highly automatic verification of hardware is at an early stage.

Uncertainty and Incompleteness: Breaking the Symmetry of Defeasible Reasoning

Abstract Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nonmonotonic reasoning with plausible reasoning based on triangular norms. A previously proposed system for reasoning with uncertainty (RUM) performs uncertain monotonic inferences on an acyclic graph. We have extended RUM to allow nonmonotonic inferences and cycles within nonmonotonic rules. By restricting the size and complexity of the nonmonotonic cycles we can still perform efficient inferences. Uncertainty measures provide a basis for deciding among multiple defaults. Different algorithms and heuristics for finding the optimal defaults are discussed.

Developing new technologies for the ARPA-Rome Planning Initiative

The article briefly describes some of the ARPI R & D programs that are focusing on technology issues in plan generation, scheduling and temporal reasoning, plan analysis, and the overall supporting infrastructure. Although we focus on individual research efforts, ARPI has encouraged researchers to integrate their work with others to provide integrated capabilities. >

It is Undecidable Whether the Knuth-Bendix Completion Procedure Generates a Crossed Pair

We reduce an instance of Turing machine acceptance to the problem of detecting whether the Knuth-Bendix completion procedure generates a crossed pair of rules. This resolves an open question posed in [5]. Our proof technique generalizes; using similar reductions, we can show that a number of other questions related to whether the Knuth-Bendix completion procedure generates certain types of rules are all undecidable. We suggest that the techniques illustrated herein may be useful in answering a number of related questions about the Knuth-Bendix completion procedure, and discuss several examples; in particular, we demonstrate how our construction provides a simple proof that the universal matching problem is undecidable for regular canonical theories, a result first proved in [4], and prove that the universal unification problem is undecidable for permutative canonical theories.