Shigeru Igarashi

Human factors in continuous time-concerned cooperative systems represented by NΣ-labeled calculus

NΣ-labeled calculus is a generalization of N-labeled calculus so as to describe time-concerned recognition, knowledge, belief and decision of humans or computer programs together with related external physical or logical phenomena. N-labeled calculus is the smallest formal system applicable to verification and analysis of cooperative real-timing systems on natural number time introduced as an adaptation of tense arithmetic (TA). A merging problem of vehicles with misunderstanding or incorrect recognition is discussed as an example of cooperating systems controlling continuously changing objects including human factor. Euler’s approximation is introduced in order to represent the continuously changing objects. Through this example, relationship among artificial intelligence, external environment and human factors is investigated.

Formal Analysis for Continous Systems Controlled by Programs

We have introduced and demonstrated a verification formalism briefly which explicitly deals with the rational time. The proof (and its verification formalism) of the example is easy and intuitive, for the conventional mathematics is used directly. The entire system of SOFA and the formal proof on FA of this example will appear elsewhere.

Formal Verification and Evaluation of Execution Time in the Envelope Theory

A logic based on the envelope theory for verification of properties of programs with evaluation of rational execution time is introduced. The truth value of proposition varies with time, so that its truth set becomes naively a set of rational time where it holds We shall, however, use a function for rational time to the set of such time sets. The “envelope” is a specialization of the closure concept attached to the lattice theory. Using this logic, properties, involving time or not, of programs can be verified more precisely and easily than using conventional methods, because concrete actual values of time length are explicitly dealt with in this relatively concise formal system. Examples follow.

A realtime human-computer ensemble system: formal representation and experiments for expressive performance

A human-computer ensemble system is one of time concerned cooperative systems, which performs secondo of an ensemble played by a computer-controlled piano cooperating with primo played by a human performer. For creating expressive performance, a rehearsal program is adopted to this system. By the rehearsal program, the system learns the tendency of the expression that the human performer thinks and/or plans. To do so, the program records his/her performance of solo and calculates the tendency, which depends on not only the performer but also the composition of music itself. Hence, it is necessary for the expressive performance to analyze the score of the composition and to experiment dependent on it. This system is an example of intelligent realtime programs appropriate for formal verification and analysis. NΣ-labeled calculus is a formal system for verification for such time-concerned programs. In this paper, a logical specification and experimental results for an expressive ensemble system will be introduced.

N{\it \Sigma}

N{\it \Sigma}

-Labeled Calculus

-labeled calculus is a formal system for representation, verification and analysis of time-concerned recognition, knowledge, belief and decision of humans or computer programs together with related external physical or logical phenomena.In this paper, a formal verification and analysis of the JAL near miss accident is presented as an example of cooperating systems controlling continuously changing objects including human factor with misunderstanding or incorrect recognition.

A matching method between music scores and performance data in a realtime person-computer ensemble system

A person-computer ensemble system is one of time-concerned cooperative systems, which performs secondo (the second part) in an ensemble played by a computer-controlled piano cooperating with primo (the leading part) played by a person performer. In the realtime performance, to determine which key is touched, or played, by the person performer, the matching algorithm between the score and the realtime input from the person performer is essential. Especially, if there are some mistouches (playing incorrectly) or other mistake, error, etc., the program does not determine which note is performed just now and which note of the secondo will be done just after now. Therefore, the matching method that corrects these mistouches is very important. In this paper, a simple and efficient matching algorithm is proposed.

Representation of Discretely Controlled Continuous Systems in Software-Oriented Formal Analysis

We have already introduced and demonstrated a new formalism SOFA to analyze and verify programs that control discretely certain continuously physical or other external systems, based on the analytical semantics. Using this formalism, program specifications and its behavior can be not only expressed easily but also directly translated into the conventional mathematics including differential equations. We obtain the actual rational time value when the next action from an observation time will rise, so that verification can be easier and more precise. Other verification systems, for example the verification diagram for reactive system, do not treat realtime system explicitly, so that they do not formulated various physical phenomena straightforward. Some examples, the leaking gas burner model and the autonomous vehicle control system, etc., will be represented, analyzed and verified formally.

Formalization of a realtime person-computer ensemble system with an effective matching algorithm

A person-computer ensemble system is one of time concerned cooperative systems, which performs secondo (the second part) in an ensemble played by a computer-controlled piano cooperating with primo (the leading part) played by a person performer. This is a good example of intelligent realtime programs appropriate for formal verification and analysis. NΣ-labeled calculus is a formal system in order to describe such systems including time-concerned recognition, knowledge, belief and decision of persons or computer programs together with related external physical or logical phenomena. In the realtime performance of music, to determine which key is played just now by the person performer, the matching algorithm between the score and the realtime input from the person performer is important. If there are some mistouching, i.e. playing an incorrect key, or other mistake, error, etc., and if the program does not detect and correct such errors, it does not determine which note is performed just now and which note of the secondo will be done just after now, and hence, it cannot control the performance speed. Therefore, the matching method including correction of these mistouches is essential. A simple but very efficient matching method with error detecting has been already developed and presented by the authors. In this paper, the formal representation of the program and its formal specification satisfied by the program written and verified in the calculus are introduced.