Reasoning about programs

This paper describes a theorem prover that embodies knowledge about programming constructs, such as numbers, arrays, lists, and expressions. The program can reason about these concepts and is used as part of a program verification system that uses the Floyd-Naur explication of program semantics. It is implemented in the qa4 language; the qa4 system allows many pieces of strategic knowledge, each expressed as a small program, to be coordinated so that a program stands forward when it is relevant to the problem at hand. The language allows clear, concise representation of this sort of knowledge. The qa4 system also has special facilities for dealing with commutative functions, ordering relations, and equivalence relations; these features are heavily used in this deductive system. The program interrogates the user and asks his advice in the course of a proof. Verifications have been found for Hoare's FIND program, a real-number division algorithm, and some sort programs, as well as for many simpler algorithms. Additional theorems have been proved about a pattern matcher and a version of Robinson's unification algorithm. The appendix contains a complete, annotated listing of the deductive system and annotated traces of several of the deductions performed by the system.     

Reasoning about agent deliberation

We present a family of sound and complete logics for reasoning about deliberation strategies for SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. The logics are variants of PDL, and allow us to prove safety and liveness properties of SimpleAPL agent programs under different deliberation strategies. We show how to axiomatise different deliberation strategies for SimpleAPL programs, and, for each strategy we prove a correspondence between the operational semantics of SimpleAPL and the models of the corresponding logic. We illustrate the utility of our approach with an example in which we show how to verify correctness properties for a simple agent program under different deliberation strategies.     

Reasoning about programs in continuation-passing style

Plotkin's _v -calculus for call-by-value programs is weaker than the -calculus for the same programs in continuation-passing style (CPS). To identify the call-by-value axioms that correspond to on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interesting in their own right. Using the new CPS transformation, we determine the precise language of CPS terms closed under -transformations, as well as the call-by-value axioms that correspond to the so-called administrative -reductions on CPS terms. Using the inverse mapping, we map the remaining and equalities on CPS terms to axioms on call-by-value terms. On the pure (constant free) set of -terms, the resulting set of axioms is equivalent to Moggi's computational -calculus. If the call-by-value language includes the control operatorsabort andcall-with-current-continuation, the axioms are equivalent to an extension of Felleisenet al.'s _v -C-calculus and to the equational subtheory of Talcott's logic IOCC.This article is a revised and extended version of the conference paper with the same title [42]. The technical report of the same title contains additional material.The authors were supported in part by NSF grant CCR 89-17022 and by Texas ATP grant 91-003604014.     

Reasoning about faulty quantum programs

We show how to use a programming language for formally describing and reasoning about errors in quantum computation. The formalisation is based on the concept of performing the correct operation with probability at least p, and the erroneous one with probability at most 1 − p. We apply the concept to two examples: Bell’s inequalities and the Deutsch–Jozsa quantum algorithm. The former is a fundamental thought experiment aimed at showing that Quantum Mechanics is not “local and realist”, and it is used in quantum cryptography protocols. We study it assuming faulty measurements, and we derive hardware reliability conditions that must be satisfied in order for the experiment to support its conclusions. The latter is a quantum algorithm for efficiently solving a classification problem for Boolean functions. The algorithm solves the problem with no error, but when we introduce faulty operations it becomes a two-sided error algorithm. Reasoning is accomplished via standard programming laws and quantum laws.     

Reasoning about probabilistic sequential programs in a probabilistic logic

We introduce a notion of strong monotonicity of probabilistic predicate transformers. This notion enables us to establish a normal form theorem for monotone probabilistic predicate transformers. Three other healthiness conditions, namely, conjunctivity, disjunctivity and continuity for probabilistic predicate transformers are also examined, and they are linked to strong monotonicity. A notion of probabilistic refinement index is proposed, and it provides us with a continuous strength spectrum of refinement relations which may be used to describe more flexible refinement between probabilistic programs. A notion of probabilistic correctness is introduced too. We give a probabilistic weakest-precondition, choice and game semantics to the contract language, and present a probabilistic generalization of the winning strategy theorem. Received: 16 April 2002 / 20 January 2003 RID="a" ID="a" This work was partly supported by the National Key Project for Fundamental Research of China (Grant No: 1998030905) and the National Foundation of Natural Sciences of China (Grant No: 60273003)     

A graded BDI agent model to represent and reason about preferences

In this research note, we introduce a graded BDI agent development framework, g-BDI for short, that allows to build agents as multi-context systems that reason about three fundamental and graded mental attitudes (i.e. beliefs, desires and intentions). We propose a sound and complete logical framework for them and some logical extensions to accommodate slightly different views on desires.     

Preference-based reasoning in BDI agent systems

An important feature of BDI agent systems is number of different ways in which an agent can achieve its goals. The choice of means to achieve the goal in made by the system at run time, depending on contextual information that is not available in advance. In this article, we explore ways that the user of an agent system can specify preferences which can be incorporated into the BDI execution process and used to guide the choices made. For example, a user of a travel system can specify a preferred airline, or a particular kind of accommodation, and the system will use this information to satisfy the goal and preferences, if possible. Preferences are specified in terms of properties of goals and resource usage, and are used to make two types of decisions: (a) select a plan when there is a choice and (b) determine the order in which subgoals of a plan should be pursued when their order is not fixed by design. We have implemented our preference framework in Jadex, and provide detailed case studies within the context of a holiday travel agent application.     

Reasoning about Prolog programs: From modes through types to assertions

We provide here a systematic comparative study of the relative strength and expressive power of a number of methods for program analysis of Prolog. Among others we show that these methods can be arranged in the following hierarchy: mode analysis type analysis monotonic properties nonmonotonic run-time properties. We also discuss a method allowing us to prove global run-time properties.     

Reasoning about Prolog programs: From modes through types to assertions

We provide here a systematic comparative study of the relative strength and expressive power of a number of methods for program analysis of Prolog. Among others we show that these methods can be arranged in the following hierarchy: mode analysis ? type analysis ? monotonic properties ? nonmonotonic run-time properties. We also discuss a method allowing us to prove global run-time properties.     

Semantics of plan revision in intelligent agents

In this paper, we give an operational and denotational semantics for a meta-language of the 3APL agent programming language. With this meta-language, various 3APL interpreters can be programmed. We prove equivalence of the operational and denotational semantics. Furthermore, we give an operational semantics for object-level 3APL. Using this semantics, we relate the 3APL meta-language to object-level 3APL by providing a specific interpreter, the semantics of which will prove to be equivalent to object-level 3APL.     

应急响应环境下基于BDI模型的Agent结构研究

基于Agent的应急响应建模仿真具有优越性和现实性,通过分析应急响应体系中Agent主体所应具有的特征——反应性、推理性、互动性和能动性,构建了基于BDI模型的反应+思考+通信的混合型Agent结构,并在NetLogo仿真平台上实现。为今后进一步研究基于Agent的应急管理建模仿真奠定研究基础,同时也为在NetLogo平台下开发基于BDI模型的Agent结构提供范式和标准。     

Reasoning about coalitional games

We develop, investigate, and compare two logic-based knowledge representation formalisms for reasoning about coalitional games. The main constructs of Coalitional Game Logic (cgl) are expressions for representing the ability of coalitions, which may be combined with expressions for representing the preferences that agents have over outcomes. Modal Coalitional Game Logic (mcgl) is a normal modal logic, in which the main construct is a modality for expressing the preferences of groups of agents. For both frameworks, we give complete axiomatisations, and show how they can be used to characterise solution concepts for coalitional games. We show that, while cgl is more expressive than mcgl, the former can only be used to reason about coalitional games with finitely many outcomes, while mcgl can be used to reason also about games with infinitely many outcomes, and is in addition more succinct. We characterise the computational complexity of satisfiability for cgl, and give a tableaux-based decision procedure.     

Reasoning about Information Change

In this paper we introduce Dynamic Epistemic Logic, which is alogic for reasoning about information change in a multi-agent system. Theinformation structures we use are based on non-well-founded sets, and canbe conceived as bisimulation classes of Kripke models. On these structures,we define a notion of information change that is inspired by UpdateSemantics (Veltman, 1996). We give a sound and complete axiomatization ofthe resulting logic, and we discuss applications to the puzzle of the dirtychildren, and to knowledge programs.     

Reasoning about synchronization in GALS systems

Correct design of interface circuits is crucial for the development of System-on-Chips (SoC) using off-the-shelf IP cores. For correct operation, an interface circuit must meet strict synchronization timing constraints, and also respect sequencing constraints between events dictated by interfacing protocols and rational clock relations. In this paper, we propose a technique for automatically analyzing the interaction between independently specified synchronization constraints and sequencing constraints between events. We show how this analysis can be used to derive delay constraints for correct operation of interface circuits in a GALS system. Our methodology allows an SoC designer to mix and match different interfacing protocols, rational clock relations and synchronization constraints for communication between a pair of modules, and automatically explore their implications on correct interface circuit design.     

Reasoning about edges in scale space

Explores the role of reasoning in early vision processing. In particular, the problem of detecting edges is addressed. The authors do not try to develop another edge detector, but rather, they study an edge detector rigorously to understand its behavior well enough to formulate a reasoning process that allow appliance of the detector judiciously to recover useful information. They present a multiscale reasoning algorithm for edge recovery: reasoning about edges in scale space (RESS). The knowledge in RESS is acquired from the theory of edge behavior in scale space and represented by a number of procedures. RESS recovers desired edge curves through a number of reasoning processes on zero crossing images at various scales. The knowledge of edge behavior in scale space enables RESS to select proper scale parameters, recover missing edges, eliminate noise or false edges, and correct the locations of edges. A brief evaluation of RESS is performed by comparing it with two well-known multistage edge detection algorithms