TY - Generic T1 - The symbolic model for algebra: functions and mechanisms Y1 - 2010 A1 - Heeffer, Albrecht ED - Magnani, Lorenzo ED - Carnielli, Walter A. ED - Pizzi, Claudio AB -

The symbolic mode of reasoning in algebra, as it emerged during the sixteenth century, can be considered as a form of model-based reasoning. In this paper we will discuss the functions and mechanisms of this model and show how the model relates to its arithmetical basis. We will argue that the symbolic model was made possible by the epistemic justification of the basic operations of algebra as practiced within the abbaco tradition. We will also show that this form of model-based reasoning facilitated the expansion of the number concept from Renaissance interpretations of number to the full notion of algebraic numbers.

JA - Model-Based Reasoning in Science and Technology PB - Springer VL - 314 SP - 519–532 SN - 9783642152221 UR - http://dx.doi.org/10.1007/978-3-642-15223-8\_29 ER - TY - Generic T1 - Adaptive Cn Logics Y1 - 2009 A1 - Batens, Diderik ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

This paper solves an old problem: to devise decent inconsistency-adaptive logics that have the \C{n} logics as their lower limit. Two kinds of logics are presented. Those of the first kind offer a maximally consistent interpretation of the premise set in as far as this is possible in view of logical considerations. At the same time, they indicate at which points further choices may be made on extra-logical grounds. The logics of the second kind allow one to introduce those choices in a defeasible way and handle them.

JA - The Many Sides of Logic PB - College Publications CY - London SP - 27–45 ER - TY - Generic T1 - Goal-Directed Tableaux Y1 - 2009 A1 - Meheus, Joke A1 - De Clercq, Kristof ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

This paper contains a new format for analytic tableaux, called goal-directed tableaux. Their main interest lies in the fact that the search for a closed tableau proceeds in a highly constrained way. The goal-directed tableaux do not form a complete decision method for propositional classical logic (because they do not sustain Ex Falso Quodlibet). For consistent sets of premises, however, they lead to the same results as the usual analytic tableaux for classical logic.

JA - The Many Sides of Logic T3 - Studies in Logic PB - College Publications CY - London VL - 21 SP - 241–256 ER - TY - Generic T1 - Prioritized Dynamic Retraction Function on Non-monotonic Information Updates Y1 - 2009 A1 - Primiero, Giuseppe ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

In this paper a model for updates on belief sets and retractions thereof is introduced using the standard format of Adaptive Logics. The core of the update retraction procedure is represented by abnormal expressions derivable in the language: they express updates with information con- tradicting previously derived contents. The adaptive strategy aims at restricting the validity of these formulas by focusing at each decreasing degree on the update which is the most rational to retract in order to re- store consistency as soon as possible. This work is related to the standard operations of retraction and withdrawal from the AGM-paradigm and the e ects of dynamic operations such as public announcement in Dynamic Epistemic Logic.

JA - The Many Sides of Logic PB - College Publications CY - London SP - 443-463 ER - TY - Generic T1 - Strategies: what's in a name? Y1 - 2009 A1 - Provijn, Dagmar ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

In this paper, I will show that Hintikka’s notion of ‘strategy’ can refer to proof-heuristic reasoning as well as to methodological reasoning forms. Stating this distinction allows for a better understanding of the notion and for an easier way to tackle the problem of formalization. Contrary to Hintikka’s opinion, heuristic reasoning can be implemented in formal proofs by means of goal-directed proof procedures. Methodological reasoning forms on the other hand can be formally represented by means of adaptive logics.

JA - The Many Sides of Logic T3 - Studies in Logic PB - College Publications VL - 21 SP - 287–306 SN - 9781904987789 ER - TY - Generic T1 - An Adaptive Logic for Pragmatic Truth Y1 - 2002 A1 - Meheus, Joke ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

This paper presents the new adaptive logic APT. APT has the peculiar property that it enables one to interpret a (possibly inconsistent) theory Gamma 'as pragmatically as possible'. The aim is to capture the idea of a partial structure (in the sense of da Costa and associates) that adequately models a (possibly inconsistent) set of beliefs Gamma. What this comes to is that APT localizes the 'consistent core' of Gamma, and that it delivers all sentences that are compatible with this core. For the core itself, APT is just as rich as Classical Logic. APT is defined from a modal adaptive logic APV that is based itself on two other adaptive logics. I present the semantics of all three systems, as well as their dynamic proof theory. The dynamic proof theory for APV is unusual (even within the adaptive logic programme) in that it incorporates two different kinds of dynamics.

JA - Paraconsistency. The Logical Way to the Inconsistent PB - Marcel Dekker CY - New York SP - 167–185 ER - TY - Generic T1 - An Inconsistency-Adaptive Proof Procedure for Logic Programming Y1 - 2002 A1 - Vermeir, Timothy ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

It is the goal of this paper to de ne a paraconsistent proof procedure that has the best of two mechanisms, in casu logic programming and inconsistency-adaptive logics. From logic programming we will maintain the ease of computing, and from adaptive logics their paraconsistency, dynamics and non-monotonicity. This will be done by combining the notion of competitor from logic programming together with the conditionallity that is common in all adaptive proofs.

JA - Paraconsistency. The Logical Way to the Inconsistent PB - Marcel Dekker CY - New York SP - 323-340 ER - TY - Generic T1 - A Logical Framework for Integrating Inconsistent Information in Multiple Databases Y1 - 2002 A1 - de Amo, Sandra A1 - Carnielli, Walter A. A1 - Marcos, João ED - Eiter, Thomas ED - Schewe, Klaus-Dieter AB -

When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. In this paper, we use one of the paraconsistent logics introduced in [9,7] (LFI1) as a logical framework to model possibly inconsistent database instances obtained by integrating different sources.We propose a method based on the sound and complete tableau proof system of LFI1 to treat both the integration process and the evolution of the integrated database submitted to users updates. In order to treat the integrated database evolution, we introduce a kind of generalized database context, the evolutionary databases, which are databases having the capability of storing and manipulating inconsistent information and, at the same time, allowing integrity constraints to change in time. We argue that our approach is sufficiently general and can be applied in most circumstances where inconsistency may arise in databases.

JA - Foundations of Information and Knowledge Systems T3 - Lecture Notes in Computer Science PB - Springer Berlin Heidelberg VL - 2284 SP - 67-84 SN - 978-3-540-43220-3 UR - http://dx.doi.org/10.1007/3-540-45758-5_5 ER - TY - Generic T1 - Ontological causes of inconsistency and a change-adaptive, logical solution Y1 - 2002 A1 - Vanackere, Guido ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

This paper reveals an implicit ontological assumption that is presupposed in common thought. This assumption results in the fact that people usually do not make any distinction between 'the object a' and 'the object a at a given moment'. This laziness causes many inconsistencies. Several attempts to solve these inconsistencies are studied, and the most natural one is elaborated, namely the one obtained by applying Classical Logic to an ontological correct domain. This solution has a drawback with respect to communication, which is solved by the change-adaptive logic CAL2. This non-monotonic, paraconsistent logic, belongs to the family of ambiguity-adaptive logics. It has the special characteristic that it solves inconsistencies by the introduction of more precise names for objects, more exactly names that refer to objects at a moment. The dynamics of the logic captures the change in objects. CAL2 has a nice proof theory, and an intuitive semantics. Interesting results and applications are commented upon, for instance those making use of the notion 'periods of invariance'. Of course, the philosophical background is discussed.

JA - Paraconsistency. The Logical Way to the Inconsistent PB - Marcel Dekker VL - 228 SP - 151–166 SN - 0824708059 ER - TY - Generic T1 - On some Remarkable Relations between Paraconsistent Logics, Modal Logics, and Ambiguity Logics Y1 - 2002 A1 - Batens, Diderik ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. ED - Loffredo D'Ottaviano, Itala M. AB -

This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL.

Three kinds of connections are illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest's LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another.

The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person's semantics for S5 as well as a description of the simple but useful and powerful AL.

JA - Paraconsistency. The Logical Way to the Inconsistent PB - Marcel Dekker CY - New York SP - 275–293 ER - TY - CONF T1 - Ex contradictione non sequitur quodlibet T2 - Proceedings of the 2000 Advanced Reasoning Forum Conference Y1 - 2001 A1 - Carnielli, Walter A. A1 - Marcos, João AB -

We summarize here the main arguments, basic research lines, and results on the foundations of the logics of formal inconsistency. These involve, in particular, some classes of well-known paraconsistent systems. We also present their semantical interpretations by way of possible-translations semantics and their applications to human reasoning and machine reasoning.

JA - Proceedings of the 2000 Advanced Reasoning Forum Conference ER - TY - Generic T1 - Tableau systems for logics of formal inconsistency T2 - Proceedings of the International Conference on Artificial Intelligence (IC-AI'2001) Y1 - 2001 A1 - Carnielli, Walter A. A1 - Marcos, João ED - Arabnia, Hamid R. AB -

The logics of formal inconsistency (LFI’s) are logics that allow to explicitly formalize the concepts of consistency and inconsistency by means of formulas of their language. Contradictoriness, on the other hand, can always be expressed in any logic, provided its language includes a symbol for negation. Besides being able to represent the distinction between contradiction and inconsistency, LFI’s are non-explosive logics, in the sense that a contradiction does not entail arbitrary statements, but yet are gently explosive, in the sense that, adjoining the additional requirement of consistency, then contradictoriness do cause explosion. Several logics can be seen as LFI’s, among them the great majority of paraconsistent systems developed under the Brazilian and Polish tradition. We present here tableau systems for some important LFI’s: bC, Ci and LFI1.

JA - Proceedings of the International Conference on Artificial Intelligence (IC-AI'2001) PB - {CSREA} Press, Athens {GA}, {USA} SP - 848-852 ER - TY - Generic T1 - A taxonomy of C-systems Y1 - 2001 A1 - Carnielli, Walter A. A1 - Marcos, João A1 - Loffredo D'Ottaviano, Itala M. ED - Carnielli, Walter A. ED - Coniglio, Marcelo E. AB -

A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of C-systems and dC-systems are defined and studied. An enormous variety of paraconsistent logics in the literature is shown to constitute C-systems.

JA - Paraconsistency. The Logical Way to the Inconsistent PB - Marcel Dekker CY - New York SP - 1-94 ER -