@incollection {D:paraty, title = {Adaptive Cn Logics}, booktitle = {The Many Sides of Logic}, year = {2009}, pages = {27{\textendash}45}, publisher = {College Publications}, address = {London}, abstract = {

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.

}, author = {Batens, Diderik}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {JK:gdt, title = {Goal-Directed Tableaux}, booktitle = {The Many Sides of Logic}, series = {Studies in Logic}, volume = {21}, year = {2009}, pages = {241{\textendash}256}, publisher = {College Publications}, address = {London}, abstract = {

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.

}, author = {Meheus, Joke and De Clercq, Kristof}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {primieroprioritized, title = {Prioritized Dynamic Retraction Function on Non-monotonic Information Updates}, booktitle = {The Many Sides of Logic}, year = {2009}, pages = {443-463}, publisher = {College Publications}, address = {London}, abstract = {

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.

}, author = {Primiero, Giuseppe}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {924546, title = {Strategies: what{\textquoteright}s in a name?}, booktitle = {The Many Sides of Logic}, series = {Studies in Logic}, volume = {21}, year = {2009}, pages = {287{\textendash}306}, publisher = {College Publications}, abstract = {

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.

}, isbn = {9781904987789}, author = {Provijn, Dagmar}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {J:alpt, title = {An Adaptive Logic for Pragmatic Truth}, booktitle = {Paraconsistency. {T}he Logical Way to the Inconsistent}, year = {2002}, pages = {167{\textendash}185}, publisher = {Marcel Dekker}, address = {New York}, abstract = {

This paper presents the new adaptive logic APT. APT has the peculiar property that it enables one to interpret a (possibly inconsistent) theory Gamma {\textquoteright}as pragmatically as possible{\textquoteright}. 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 {\textquoteright}consistent core{\textquoteright} 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.

}, author = {Meheus, Joke}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {vermeir2002inconsistency, title = {An Inconsistency-Adaptive Proof Procedure for Logic Programming}, booktitle = {Paraconsistency. The Logical Way to the Inconsistent}, year = {2002}, pages = {323-340}, publisher = {Marcel Dekker}, address = {New York}, abstract = {

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.

}, author = {Vermeir, Timothy}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {402884, title = {Ontological causes of inconsistency and a change-adaptive, logical solution}, booktitle = {Paraconsistency. The Logical Way to the Inconsistent}, volume = {228}, year = {2002}, pages = {151{\textendash}166}, publisher = {Marcel Dekker}, abstract = {

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 {\textquoteright}the object a{\textquoteright} and {\textquoteright}the object a at a given moment{\textquoteright}. 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 {\textquoteright}periods of invariance{\textquoteright}. Of course, the philosophical background is discussed.

}, isbn = {0824708059}, author = {Vanackere, Guido}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {D:camp, title = {On some Remarkable Relations between Paraconsistent Logics, Modal Logics, and Ambiguity Logics}, booktitle = {Paraconsistency. {T}he Logical Way to the Inconsistent}, year = {2002}, pages = {275{\textendash}293}, publisher = {Marcel Dekker}, address = {New York}, abstract = {

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{\textquoteright}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{\textquoteright}s semantics for S5 as well as a description of the simple but useful and powerful AL.

}, author = {Batens, Diderik}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @incollection {carnielli2001taxonomy, title = {A taxonomy of C-systems}, booktitle = {Paraconsistency. The Logical Way to the Inconsistent}, year = {2001}, pages = {1-94}, publisher = {Marcel Dekker}, address = {New York}, abstract = {

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.

}, author = {Carnielli, Walter A. and Marcos, Jo{\~a}o and Loffredo D{\textquoteright}Ottaviano, Itala M.}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E.} }