Didattica del ragionamento: un esempio di deduzione logica in ambiente Mathematica

Si mostra come, in un ambiente adeguato per il calcolo simbolico, si possano introdurre elementi di programmazione logica, “traducendo” una teoria in un insieme di definizioni di funzioni. Dal punto di vista didattico, tale riduzione della programmazione logica a programmazione funzionale risulta utile per l’ampliamento dell’uso di strumenti informatici all’ambito della logica matematica. Inoltre, un ulteriore obiettivo è quello di facilitare, attraverso tali strumenti, lo sviluppo di competenze non solo nell’ambito del calcolo numerico-algebrico ma anche in quello dell’ informazione di tipo assertivo-logico. Il nostro punto di vista è che nella sperimentazione didattica sia possibile riferirsi alla logica non solo per quanto riguarda il calcolo proposizionale ma anche al suo aspetto deduttivo. E’ necessario evidenziare come il metodo assiomatico sia presente nella vita di tutti i giorni. Nozioni come quelle di “sistema di assiomi” e di “teorema” devono essere interpretate in termini di informazione disponibile, (in generale non completa) circa situazioni della vita reale, e di conseguenze che si possono ricavare a partire da tale informazione

Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Los--Tarski and the Chang--Los--Suszko preservation theorems follow

Fuzzy Logic in Two Non-Interacting Tanks in Series

Two Non-Interacting Tanks is commonly used in the petrochemical industry especially when it involves chemical reaction. Most chemical reaction needs optimum time to achieve the target conversion rate, so precise and controlled retention time of the chemicals in the tanks/reactors is very essential. This leads to the development of my project where I will compare fuzzy logic control, an advance control system and compare it with the conventional controller, which is the P1D controller. Fuzzy Controller is basically a controller that mimics a human in term of decision making by installing a range of human "decision" based on condition that we have introduced to the controller. PID Controller however is a controller based on the mathematical process modeling of the system & it will measure the error of the system from the set-point and perform a calculation for corrective action based on the PID equation. The results of the simulation will be compared based on the settling time, overshoot peak and maximum level at steady state of the tanks

Comparison of two kinds of fuzzy arithmetic, LR and OFN, applied to fuzzy observation of the cofferdam water level

This paper presents certain important aspects of the fuzzy logic extension, one of which is OFN. It includes basic definitions of that discipline. It also compares fuzzy logic arithmetic with the arithmetic of ordered fuzzy numbers in L-R notation. Computational experiments were based on fuzzy observation of the impounding basin. The results of the study show that there is a connection between the order of OFN number and trend of changes in the environment. The experiment was carried out using computer software developed specially for that purpose. When comparing the arithmetic of fuzzy numbers in L-R notation with the arithmetic of ordered fuzzy numbers on the grounds of the experiment, it has been concluded that with fuzzy numbers it is possible to expand the scope of solutions in comparison to fuzzy numbers in classic form. The symbol of OFN flexibility is the possibility to determine the X number that always satisfies the equation A+X=C, regardless of the value of arguments. Operations performed on OFN are less complicated, as they are performed in the same way regardless the sign of the input data and their results are more accurate in the majority of cases. The promising feature of ordered fuzzy numbers is their lack of rapidly growing fuzziness. Authors expect to see implication of that fact in practice in the near future

Vagueness and Formal Fuzzy Logic: Some Criticisms

In the common man reasoning the presence of vague predicates is pervasive and under the name “fuzzy logic in narrow sense” or “formal fuzzy logic” there are a series of attempts to formalize such a kind of phenomenon. This paper is devoted to discussing the limits of these attempts both from a technical point of view and with respect the original and principal task: to define a mathematical model of the vagueness. For example, one argues that, since vagueness is necessarily connected with the intuition of the continuum, we have to look at the order-based topology of the interval [0,1] and not at the discrete topology of the set {0,1}. In accordance, in switching from classical logic to a logic for the vague predicates, we cannot avoid the use of the basic notions of real analysis as, for example, the ones of “approximation“, “convergence“, “continuity“. In accordance, instead of defining the compactness of the logical consequence operator and of the deduction operator in terms of finiteness, we have to define it in terms of continuity. Also, the effectiveness of the deduction apparatus has to be defined by using the tools of constructive real analysis and not the one of recursive arithmetic. This means that decidability and semi-decidability have to be defined by involving effective limit processes and not by finite steps stopping processes

On the existence of free models in fuzzy universal Horn classes

This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on some relevant notions in logic programming. We introduce the notion of term structure associated to a set of formulas in the fuzzy context and we show the existence of free models in fuzzy universal Horn classes. We prove that every equality-free consistent universal Horn fuzzy theory has a Herbrand model

Fuzzy Logic in Two Non-Interacting Tanks in Series

Two Non-Interacting Tanks is commonly used in the petrochemical industry especially when it involves chemical reaction. Most chemical reaction needs optimum time to achieve the target conversion rate, so precise and controlled retention time of the chemicals in the tanks/reactors is very essential. This leads to the development of my project where I will compare fuzzy logic control, an advance control system and compare it with the conventional controller, which is the P1D controller. Fuzzy Controller is basically a controller that mimics a human in term of decision making by installing a range of human "decision" based on condition that we have introduced to the controller. PID Controller however is a controller based on the mathematical process modeling of the system & it will measure the error of the system from the set-point and perform a calculation for corrective action based on the PID equation. The results of the simulation will be compared based on the settling time, overshoot peak and maximum level at steady state of the tanks

A Hybrid Fuzzy Genetic Algorithm for an Adaptive Traffic Signal System

This paper presents a hybrid algorithm that combines Fuzzy Logic Controller (FLC) and Genetic Algorithms (GAs) and its application on a traffic signal system. FLCs have been widely used in many applications in diverse areas, such as control system, pattern recognition, signal processing, and forecasting. They are, essentially, rule-based systems, in which the definition of these rules and fuzzy membership functions is generally based on verbally formulated rules that overlap through the parameter space. They have a great influence over the performance of the system. On the other hand, the Genetic Algorithm is a metaheuristic that provides a robust search in complex spaces. In this work, it has been used to adapt the decision rules of FLCs that define an intelligent traffic signal system, obtaining a higher performance than a classical FLC-based control. The simulation results yielded by the hybrid algorithm show an improvement of up to 34% in the performance with respect to a standard traffic signal controller, Conventional Traffic Signal Controller (CTC), and up to 31% in the comparison with a traditional logic controller, FLC

Test moment determination design in active robot learning

A thesis submitted to the University of Bedfordshire, in fulfilment of the requirements for the degree of Master of Science by researchIn recent years, service robots have been increasingly used in people's daily live. These robots are autonomous or semiautonomous and are able to cooperate with their human users. Active robot learning (ARL) is an approach to the development of beliefs for the robots on their users' intention and preference, which is needed by the robots to facilitate the seamless cooperation with humans. This approach allows a robot to perform tests on its users and to build up the high-order beliefs according to the users' responses. This study carried out primary research on designing the test moment determination component in ARL framework. The test moment determination component is used to decide right moment of taking a test action. In this study, an action plan theory was suggested to synthesis actions into a sequence, that is, an action plan, for a given task. All actions are defined in a special format of precondition, action, post-condition and testing time. Forward chaining reasoning was introduced to establish connection between the actions and to synthesis individual actions into an action plan, corresponding to the given task. A simulation environment was set up where a human user and a service robot were modelled using MATLAB. Fuzzy control was employed for controlling the robot to carry out the cooperative action. In order to examine the effect of test moment determination component, simulations were performed to execute a scenario where a robot passes on an object to a human user. The simulation results show that an action plan can be formed according to provided conditions and executed by simulated models properly. Test actions were taken at the moment determined by the test moment determination component to find the human user's intention