On the notion of negation in certain non-classical propositional logics

The purpose of this study is to investigate some aspects of how negation functions in certain non-classical propositional logics. These include the intuitionistic system developed by Heyting, the minimal calculus proposed by Johansson, and various intermediate logics between the minimal and the classical systems. Part I contains the new results which can be grouped into two classes: extension-criteria results and infinite chain results. In the first group criteria are given for answering the question: when do formulae added to the axioms of the minimal calculus as extra axioms extend the minimal calculus to various known intermediate logics? One of the results in this group (THEOREM 1 in Chapter II, Section 1) is a generalization of a result of Jankov. In the second group certain intermediate logics are defined which form infinite chains between well-known logical systems. One of the results here (THEOREM 1 in Chapter II, Section 2) is a generalization of a result of McKay. In Part II the new results are discussed from the viewpoint of negation. It is rather difficult, however, to draw definite conclusions which are acceptable to all. For these depend on, and are closely bound up with, certain basic philosophical presuppositions which are neither provable, nor disprovable in a strict sense. Taking an essentially classical position, it is argued that the logics appearing in the defined infinite chains are such that they diverge only in the vicinity of negation, and the notions of negation in them are simply ordered in a sense which is specified during the discussion. In Appendix I a number of conjectures are formulated in connection with the new results.<p

The many-valued theorem prover 3TAP. 3rd. edition

This is the 3TAP handbook. 3TAP is a many-valued tableau-based theorem prover developed at the University of Karlsruhe. The handbook serves a triple purpose: first, it documents the history and development of the prover 3TAP; second, it provides a user\u27s manual, and third it is intended as a reference manual for future developers, including porting hints. This version of the handbook describes 3TAP Version 3.0 as of September 30,1994

50 years a biomedical engineer remembering a long and fascinating journey

Looking back at one point of life appears as a nice exercise to round out and summarize. However, the objective should not be simply to tell a story; it must transmit a message to the young. To start with, two concepts are useful: Respect for others begins when you learn to laugh at yourself and, taken from an old saying, I did not want to be poor ... but money wouldn't make me rich. After elementary and high schools, during times of turmoil, I describe my engineering school years at the University of Buenos Aires and a working experience in an international telecommunications company. Significant events taught me a concept, rooted in another motto: Isn't this house nice? It is my house, and I love it very much. In 1960, I began my activities in the USA. A couple of bad decisions resulted in significant events for me teaching me an important truth: "Beware of golden promises; time is the most precious asset". Finally, in 1972, settled down in Tucumán until retirement in 2001, a long period of productive activity came about, not without difficulties and also stained by a dark political interval. Crises seem to characterize our generations in Argentina. Non-the-less, there were some real accomplishments: an undergraduate program in BME and a National BME Society (SABI) plus an archive of specialized published material. After spending time following retirement in Peru and Italy, my current activity came as unexpected dessert at the University of Buenos Aires, with a small research group, so offering the opportunity of transmitting what I still have available

Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

A structural model interpretation of Wright's NESS test

Although understanding causation is an essential part of nearly every problem domain, it has resisted formal treatment in the languages of logic, probability, and even statistics. Autonomous artificially intelligent agents need to be able to reason about cause and effect. One approach is to provide the agent with formal, computational notions of causality that enable the agent to deduce cause and effect relationships from observations. During the 1990s, formal notions of causality were pursued within the AI community by many researchers, notably by Judea Pearl. Pearl developed the formal language of structural models for reasoning about causation. Among the problems he addressed in this formalism was a problem common to both AI and law, the attribution of causal responsibility or actual causation. Pearl and then Halpern and Pearl developed formal definitions of actual causation in the language of structural models. Within the law, the traditional test for attributing causal responsibility is the counterfactual "but-for" test, which asks whether, but for the defendant's wrongful act, the injury complained of would have occurred. This definition conforms to common intuitions regarding causation in most cases, but gives non-intuitive results in more complex situations where two or more potential causes are present. To handle such situations, Richard Wright defined the NESS Test. Pearl claims that the structural language is an appropriate language to capture the intuitions that motivate the NESS test. While Pearl's structural language is adequate to formalize the NESS test, a recent result of Hopkins and Pearl shows that the Halpern and Pearl definition fails to do so, and this thesis develops an alternative structural definition to formalize the NESS test