Necesidad lógica y lógica condicional

El artículo pretende, en primer lugar, caracterizar brevemente la idea de verdad necesaria en Leibniz a los efectos de mostrar cómo en el desarrollo de las investigaciones lógicas ella se ha ido debilitando al extremo de convertirse en una de las tantas posibles interpretaciones del operador de necesidad. Se muestra, además, que ello ha sucedido tanto en los sistemas generados a partir de las semánticas de Kripke para la lógica modal clásica como para los sistemas de lógica, para los condicionales contrafácticos de David Lewis y para los condicionales derrotables de Carlos Alchourrón.

Necesidad lógica y lógica condicional

El artículo pretende, en primer lugar, caracterizar brevemente la idea de verdad necesaria en Leibniz a los efectos de mostrar cómo en el desarrollo de las investigaciones lógicas ella se ha ido debilitando al extremo de convertirse en una de las tantas posibles interpretaciones del operador de necesidad. Se muestra, además, que ello ha sucedido tanto en los sistemas generados a partir de las semánticas de Kripke para la lógica modal clásica como para los sistemas de lógica, para los condicionales contrafácticos de David Lewis y para los condicionales derrotables de Carlos Alchourrón.

A deontic analysis of inter -organizational control requirements

This research focuses on the design and verification of inter-organizational controls. Instead of looking at a documentary procedure, which is the flow of documents and data among the parties, the research examines the underlying deontic purpose of the procedure, the so-called deontic process, and identifies control requirements to secure this purpose. The vision of the research is a formal theory for streamlining bureaucracy in business and government procedures. ^ Underpinning most inter-organizational procedures are deontic relations, which are about rights and obligations of the parties. When all parties trust each other, they are willing to fulfill their obligations and honor the counter parties’ rights; thus controls may not be needed. The challenge is in cases where trust may not be assumed. In these cases, the parties need to rely on explicit controls to reduce their exposure to the risk of opportunism. However, at present there is no analytic approach or technique to determine which controls are needed for a given contracting or governance situation. ^ The research proposes a formal method for deriving inter-organizational control requirements based on static analysis of deontic relations and dynamic analysis of deontic changes. The formal method will take a deontic process model of an inter-organizational transaction and certain domain knowledge as inputs to automatically generate control requirements that a documentary procedure needs to satisfy in order to limit fraud potentials. The deliverables of the research include a formal representation namely Deontic Petri Nets that combine multiple modal logics and Petri nets for modeling deontic processes, a set of control principles that represent an initial formal theory on the relationships between deontic processes and documentary procedures, and a working prototype that uses model checking technique to identify fraud potentials in a deontic process and generate control requirements to limit them. Fourteen scenarios of two well-known international payment procedures—cash in advance and documentary credit—have been used to test the prototype. The results showed that all control requirements stipulated in these procedures could be derived automatically.^

A Deontic Analysis of Inter-Organizational Control Requirements

This research focuses on the design and verification of inter-organizational controls. Instead of looking at a documentary procedure, which is the flow of documents and data among the parties, the research examines the underlying deontic purpose of the procedure, the so-called deontic process, and identifies control requirements to secure this purpose. The vision of the research is a formal theory for streamlining bureaucracy in business and government procedures. Underpinning most inter-organizational procedures are deontic relations, which are about rights and obligations of the parties. When all parties trust each other, they are willing to fulfill their obligations and honor the counter parties’ rights; thus controls may not be needed. The challenge is in cases where trust may not be assumed. In these cases, the parties need to rely on explicit controls to reduce their exposure to the risk of opportunism. However, at present there is no analytic approach or technique to determine which controls are needed for a given contracting or governance situation. The research proposes a formal method for deriving inter-organizational control requirements based on static analysis of deontic relations and dynamic analysis of deontic changes. The formal method will take a deontic process model of an inter-organizational transaction and certain domain knowledge as inputs to automatically generate control requirements that a documentary procedure needs to satisfy in order to limit fraud potentials. The deliverables of the research include a formal representation namely Deontic Petri Nets that combine multiple modal logics and Petri nets for modeling deontic processes, a set of control principles that represent an initial formal theory on the relationships between deontic processes and documentary procedures, and a working prototype that uses model checking technique to identify fraud potentials in a deontic process and generate control requirements to limit them. Fourteen scenarios of two well-known international payment procedures -- cash in advance and documentary credit -- have been used to test the prototype. The results showed that all control requirements stipulated in these procedures could be derived automatically.

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic.

Two Consistent Many-Valued Logics for Paraconsistent Phenomena

In this reviewing paper, we recall the main results of our papers [24, 31] where we introduced two paraconsistent semantics for Pavelka style fuzzy logic. Each logic formula a is associated with a 2 x 2 matrix called evidence matrix. The two semantics are consistent if they are seen from 'outside'; the structure of the set of the evidence matrices M is an MV-algebra and there is nothing paraconsistent there. However, seen from "inside,' that is, in the construction of a single evidence matrix paraconsistency comes in, truth and falsehood are not each others complements and there is also contradiction and lack of information (unknown) involved. Moreover, we discuss the possible applications of the two logics in real-world phenomena.

Variants of temporal defeasible logics for modelling norm modifications

This paper proposes some variants of Temporal Defeasible Logic (TDL) to reason about normative modifications. These variants make it possible to differentiate cases in which, for example, modifications at some time change legal rules but their conclusions persist afterwards from cases where also their conclusions are blocked.

From aesthetic principles to collective sentiments: The logics of everyday judgements of taste

Contemporary research into the sociology of taste has, following Bourdieu (1984), primarily emphasised the role of social position, or more broadly as implicated int he reproduction of social inequality. We argue that although important, such a preoccupation with the social distribution of objectified tastes--for example in music, literature, and art--has been at the expense of investigating the everyday perceptual schemes and resources used by actors to accomplish a judgement of taste. Our argument is traced using a range of classical and contemporary literature which deals with the personal/collective tension in taste, aesthetics and fashion. We use data from a recent national survey to investigate how a sample of ordinary fashion. We use data from a recent national survey to investigate how a sample of ordinary actors understand the categories of 'good' and 'bad' taste. The analysis shows a strong collective strand in everyday definitions of taste, often linked to moral codes of interpersonal conduct. Also, taste is largely defined by people as a strategy for managing relations with others, and as a mode of self-discipline which relies on the mastery of a number of general principles that are resources for people to position their own tastes within an imagined social sphere. This paper proposes a schematic model which accounts for the range of discriminatory resources used to make judgements of taste.

Symbolic Knowledge Extraction from Trained Neural Networks Governed by Lukasiewicz Logics

This work describes a methodology to extract symbolic rules from trained neural networks. In our approach, patterns on the network are codified using formulas on a Lukasiewicz logic. For this we take advantage of the fact that every connective in this multi-valued logic can be evaluated by a neuron in an artificial network having, by activation function the identity truncated to zero and one. This fact simplifies symbolic rule extraction and allows the easy injection of formulas into a network architecture. We trained this type of neural network using a back-propagation algorithm based on Levenderg-Marquardt algorithm, where in each learning iteration, we restricted the knowledge dissemination in the network structure. This makes the descriptive power of produced neural networks similar to the descriptive power of Lukasiewicz logic language, minimizing the information loss on the translation between connectionist and symbolic structures. To avoid redundance on the generated network, the method simplifies them in a pruning phase, using the "Optimal Brain Surgeon" algorithm. We tested this method on the task of finding the formula used on the generation of a given truth table. For real data tests, we selected the Mushrooms data set, available on the UCI Machine Learning Repository.