Building and Refining Abstract Planning Cases by Change of Representation Language

ion is one of the most promising approaches to improve the performance of problem solvers. In several domains abstraction by dropping sentences of a domain description -- as used in most hierarchical planners -- has proven useful. In this paper we present examples which illustrate significant drawbacks of abstraction by dropping sentences. To overcome these drawbacks, we propose a more general view of abstraction involving the change of representation language. We have developed a new abstraction methodology and a related sound and complete learning algorithm that allows the complete change of representation language of planning cases from concrete to abstract. However, to achieve a powerful change of the representation language, the abstract language itself as well as rules which describe admissible ways of abstracting states must be provided in the domain model. This new abstraction approach is the core of Paris (Plan Abstraction and Refinement in an Integrated System), a system in which abstract planning cases are automatically learned from given concrete cases. An empirical study in the domain of process planning in mechanical engineering shows significant advantages of the proposed reasoning from abstract cases over classical hierarchical planning.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Data Abstraction Mechanisms in Sina/st

This paper describes a new data abstraction mechanism in an object-oriented model of computing. The data abstraction mechanism described here has been devised in the context of the design of Sina/st language. In Sina/st no language constructs have been adopted for specifying inheritance or delegation, but rather, we introduce simpler mechanisms that can support a wide range of code sharing strategies without selecting one among them as a language feature. Sina/st also provides a stronger data encapsulation than most of the existing object-oriented languages. This language has been implemented on the SUN 3 workstation using Smalltalk

On Verifying Complex Properties using Symbolic Shape Analysis

One of the main challenges in the verification of software systems is the analysis of unbounded data structures with dynamic memory allocation, such as linked data structures and arrays. We describe Bohne, a new analysis for verifying data structures. Bohne verifies data structure operations and shows that 1) the operations preserve data structure invariants and 2) the operations satisfy their specifications expressed in terms of changes to the set of objects stored in the data structure. During the analysis, Bohne infers loop invariants in the form of disjunctions of universally quantified Boolean combinations of formulas. To synthesize loop invariants of this form, Bohne uses a combination of decision procedures for Monadic Second-Order Logic over trees, SMT-LIB decision procedures (currently CVC Lite), and an automated reasoner within the Isabelle interactive theorem prover. This architecture shows that synthesized loop invariants can serve as a useful communication mechanism between different decision procedures. Using Bohne, we have verified operations on data structures such as linked lists with iterators and back pointers, trees with and without parent pointers, two-level skip lists, array data structures, and sorted lists. We have deployed Bohne in the Hob and Jahob data structure analysis systems, enabling us to combine Bohne with analyses of data structure clients and apply it in the context of larger programs. This report describes the Bohne algorithm as well as techniques that Bohne uses to reduce the ammount of annotations and the running time of the analysis

Embodied Active Learning of Relational State Abstractions for Bilevel Planning

State abstraction is an effective technique for planning in robotics environments with continuous states and actions, long task horizons, and sparse feedback. In object-oriented environments, predicates are a particularly useful form of state abstraction because of their compatibility with symbolic planners and their capacity for relational generalization. However, to plan with predicates, the agent must be able to interpret them in continuous environment states (i.e., ground the symbols). Manually programming predicate interpretations can be difficult, so we would instead like to learn them from data. We propose an embodied active learning paradigm where the agent learns predicate interpretations through online interaction with an expert. For example, after taking actions in a block stacking environment, the agent may ask the expert: "Is On(block1, block2) true?" From this experience, the agent learns to plan: it learns neural predicate interpretations, symbolic planning operators, and neural samplers that can be used for bilevel planning. During exploration, the agent plans to learn: it uses its current models to select actions towards generating informative expert queries. We learn predicate interpretations as ensembles of neural networks and use their entropy to measure the informativeness of potential queries. We evaluate this approach in three robotic environments and find that it consistently outperforms six baselines while exhibiting sample efficiency in two key metrics: number of environment interactions, and number of queries to the expert. Code: https://tinyurl.com/active-predicatesComment: Conference on Lifelong Learning Agents (CoLLAs) 202

Syntactic Abstraction of B Models to Generate Tests

In a model-based testing approach as well as for the verification of properties, B models provide an interesting solution. However, for industrial applications, the size of their state space often makes them hard to handle. To reduce the amount of states, an abstraction function can be used, often combining state variable elimination and domain abstractions of the remaining variables. This paper complements previous results, based on domain abstraction for test generation, by adding a preliminary syntactic abstraction phase, based on variable elimination. We define a syntactic transformation that suppresses some variables from a B event model, in addition to a method that chooses relevant variables according to a test purpose. We propose two methods to compute an abstraction A of an initial model M. The first one computes A as a simulation of M, and the second one computes A as a bisimulation of M. The abstraction process produces a finite state system. We apply this abstraction computation to a Model Based Testing process.Comment: Tests and Proofs 2010, Malaga : Spain (2010

From Logical Calculus to Logical Formality—What Kant Did with Euler’s Circles

John Venn has the “uneasy suspicion” that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kant’s “disastrous effect on logical method,” namely the “strictest preservation [of logic] from mathematical encroachment.” Kant’s actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Euler’s circles and comparing it with Euler’s own use. I do so in light of the developments in logical calculus from G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations

Predicate Abstraction with Indexed Predicates

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International Conference on Verification, Model Checking and Abstract Interpretation (VMCAI'04), LNCS 2937, pages = 267--28