Abstract Domains and Solvers for Sets Reasoning

This chapter investigates a formal approach to the verification of non-functional software requirements that are crucial in Service-oriented Systems, like portability, time and space efficiency, and dependability/robustness. The key-idea is the notion of observable, i.e., an abstraction of the concrete semantics when focusing on a behavioral property of interest. By applying an abstract interpretation-based static analysis of the source program, and by a suitable choice of abstract domains, it is possible to design formal and effective tools for non-functional requirements validation.

Download Full-text

PIQA: Reasoning about Physical Commonsense in Natural Language

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i05.6239 ◽

2020 ◽

Vol 34 (05) ◽

pp. 7432-7439

Author(s):

Yonatan Bisk ◽

Rowan Zellers ◽

Ronan Le bras ◽

Jianfeng Gao ◽

Yejin Choi

Keyword(s):

Natural Language ◽

Question Answering ◽

Natural Language Understanding ◽

Physical World ◽

Future Research ◽

Physical Interaction ◽

Commonsense Reasoning ◽

Cotton Swab ◽

Language Understanding ◽

Abstract Domains

To apply eyeshadow without a brush, should I use a cotton swab or a toothpick? Questions requiring this kind of physical commonsense pose a challenge to today's natural language understanding systems. While recent pretrained models (such as BERT) have made progress on question answering over more abstract domains – such as news articles and encyclopedia entries, where text is plentiful – in more physical domains, text is inherently limited due to reporting bias. Can AI systems learn to reliably answer physical commonsense questions without experiencing the physical world?In this paper, we introduce the task of physical commonsense reasoning and a corresponding benchmark dataset Physical Interaction: Question Answering or PIQA. Though humans find the dataset easy (95% accuracy), large pretrained models struggle (∼75%). We provide analysis about the dimensions of knowledge that existing models lack, which offers significant opportunities for future research.

Download Full-text

Modular Constraint Solver Cooperation via Abstract Interpretation

Theory and Practice of Logic Programming ◽

10.1017/s1471068420000162 ◽

2020 ◽

Vol 20 (6) ◽

pp. 848-863

Author(s):

PIERRE TALBOT ◽

ÉRIC MONFROY ◽

CHARLOTTE TRUCHET

Keyword(s):

Abstract Interpretation ◽

Job Shop ◽

Job Shop Scheduling ◽

Constraint Solving ◽

Bound Constraints ◽

Ordered Structures ◽

Constraint Solver ◽

Abstract Domains ◽

Theoretical Foundations ◽

Modular Framework

AbstractCooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i) interval propagators completion that allows abstract domains to exchange bound constraints, and (ii) delayed product which exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logic programming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose the shared product to combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem.

Download Full-text

A backward analysis for constraint logic programs

Theory and Practice of Logic Programming ◽

10.1017/s1471068402001436 ◽

2002 ◽

Vol 2 (4-5) ◽

pp. 517-547 ◽

Cited By ~ 13

Author(s):

ANDY KING ◽

LUNJIN LU

Keyword(s):

Ad Hoc ◽

Abstract Interpretation ◽

Logic Program ◽

Control Flow ◽

Third Party ◽

Logic Programs ◽

Abstract Domains ◽

Constraint Logic Programs ◽

Backward Analysis ◽

Computational Properties

One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If the logic program does not come with any documentation, then the programmer is forced to either experiment with queries in an ad hoc fashion or trace the control-flow of the program (backward) to infer the modes in which a predicate must be called so as to avoid an instantiation error. This paper presents an abstract interpretation scheme that automates the latter technique. The analysis presented in this paper can infer moding properties which if satisfied by the initial query, come with the guarantee that the program and query can never generate any moding or instantiation errors. Other applications of the analysis are discussed. The paper explains how abstract domains with certain computational properties (they condense) can be used to trace control-flow backward (right-to-left) to infer useful properties of initial queries. A correctness argument is presented and an implementation is reported.

Download Full-text