Marcelo Esteban Coniglio | Universidade Estadual de Campinas (original) (raw)

Papers by Marcelo Esteban Coniglio

Research paper thumbnail of Recovery operators, paraconsistency and duality

CLE e-Prints, 2017

There are two foundational but not properly developed ideas in da Costa's approach to paraconsist... more There are two foundational but not properly developed ideas in da Costa's approach to paraconsistency: the 'well-behavedness' operator and the duality between paraconsistent and intuitionistic logics. The aim of this paper is to present how these two ideas can be developed by Logics of Formal Inconsistency (LFIs) and Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, and LFUs recover the validity of the excluded middle in a paracomplete scenario. We will present two formal systems, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core – in the case studied here, classical positive propositional logic (CPL+). mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. Then, we combine these two logics obtaining logics of formal inconsistency and undeterminedness (LFIUs), called mbCD and mbCDE. The swap structures semantics framework for LFIs, is adapted here for LFUs and LFIUs. This semantics allows us to prove the decidability of the proposed systems by means of finite non-deterministic matrices.

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Research paper thumbnail of Non-deterministic algebraization of logics by swap structures

arXiv:1708.08499 [math.LO], 2017

Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Ma... more Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Mathematics and in Computer Science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several logics of formal inconsistency (or LFIs) which cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multi-algebras in a suitable way. A decomposition theorem similar to Birkhoff's representation theorem is obtained for each class of swap structures. Moreover , when applied to the 3-valued algebraizable logic J3 the usual class of algebraic models is recovered, and the swap structures semantics became twist-structures semantics (as introduced by Fidel-Vakarelov). This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, which is closely connected with Kalman's functor, suggests that swap structures can be considered as non-deterministic twist structures, opening so interesting possibilities for dealing with non-algebraizable logics by means of multi-algebraic semantics.

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Research paper thumbnail of Relevant Information and Relevant Logic

In: Proceedings of the 6th "Dr. Antonio A. R. Monteiro" Congress of Mathematics, pp. 119-127. Bahia Blanca, Argentina, 2001. , 2001

In this paper we define and develop an algebraic structure associated with the concept of systems... more In this paper we define and develop an algebraic structure associated with the concept of systems of relevant information (SRI), which is a variant of the semilattice semantics proposed by A. Urquhart in [6]. The propositional relevant logic RP is introduced as the syntactical counterpart of the SRI-structures. This logic has a primitive-recursive decision procedure. The idea behind this logic is that of "Relevant Deduction" , in which each premise is a block of information relevant to the conclusion. Finally, we prove that the class of SRI-structures is a sound and complete semantics for the logic RP .

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Research paper thumbnail of On formal aspects of the epistemic approach to paraconsistency

This paper reviews the central points and presents some recent developments of the epistemic appr... more This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LETJ ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson's logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for both BLE and LETJ . The meanings of the connectives of BLE and LETJ , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A
formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LETJ is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed.

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Research paper thumbnail of Formal (In)consistency, Abduction and Modalities

Springer Handbook of Model-Based Science, 2017

This chapter proposes a study of philosophical and technical aspects of logics of formal inconsis... more This chapter proposes a study of philosophical and technical aspects of logics of formal inconsistency (LFI s), a family of paraconsistent logics that have resources to express the notion of consistency inside the object language. This proposal starts by presenting an epistemic approach to paraconsistency according to which the acceptance of a pair of contradictory propositions A and \(\neg A\) does not imply accepting both as true. It is also shown how LFIs may be connected to the problem of abduction by means of tableaux that indicate possible solutions for abductive problems. The connection between the notions of modalities and consistency is also worked out, and some LFIs based on positive modal logics (called anodic modal logics), are surveyed, as well as their extensions supplied with different degrees of negations (called cathodic modal logics). Finally, swap structures are explained as new and interesting semantics for the LFIs, and shown to be as a particular important case of the well-known possible-translations semantics (PTS ).

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Research paper thumbnail of Modal logic S4 as a paraconsistent logic with a topological semantics

Logic and Computation: Essays in Honour of Amilcar Sernadas, Jul 5, 2017

In this paper the propositional logic LTop is introduced, as an extension of classical propositio... more In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency.

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Research paper thumbnail of AGM-like paraconsistent belief change

Logic Journal of the IGPL, 2017

Two systems of belief change based on paraconsistent logics are introduced in this article by mea... more Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo, is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations.

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Research paper thumbnail of Errata and Addenda to ‘Finite non-deterministic semantics for some modal systems’

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly re... more In this note, an error in the axiomatization of Ivlev’s modal system Sa+
which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems” (CFP2015), is fixed. Additionally, some axioms proposed in (CFP2015) were slightly modified. All the technical results in (CFP2015) which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in (CFP2015) is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed.

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Research paper thumbnail of Towards an hyperalgebraic theory of non-algebraizable logics

CLE e-Prints, Vol. 16 N. 4, Oct 14, 2016

Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of L... more Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics of swap structures for LFIs, which are Nmatrices defined over triples in a Boolean algebra, generalizing Avron's semantics. In this paper we develop the first steps towards the possibility of defining an algebraic theory of swap structures for LFIs, by adapting concepts of universal algebra to multialgebras in a suitable way.

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Research paper thumbnail of Non-deterministic algebras and algebraization of logics

Filosofia da Linguagem e da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese), Dec 2015

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Research paper thumbnail of Contradictions in reasoning: an evil or a blessing?

The purpose of this short essay is to explain the role of contradictions in the development of sc... more The purpose of this short essay is to explain the role of contradictions in the development of scientific theories. We argue that contradictions are not to be seen as a signal of defeat, but overall as a chance for improvement.

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Research paper thumbnail of Paraconsistent Belief Revision based on a formal consistency operator

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both define... more In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not
necessarily related to the notion of formal consistency.

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Research paper thumbnail of Paraconsistent Belief Revision based on a formal consistency operator

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined... more In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency – not
necessarily related to the notion of formal consistency.

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Research paper thumbnail of On the set of intermediate logics between the truth and degree preserving Lukasiewicz logics

The aim of this paper is to explore the class of intermediate logics between the truth-preserving... more The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L ≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L ≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in [0, 1], but we show there are intermediate logics falling outside this family. Finally, we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A, F) such that A is a finite MV-algebra and F is a lattice filter.

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Research paper thumbnail of On the ordered Dedekind real numbers in toposes

Why is this a Proof? Festschrift for Luiz Carlos Pereira, Jun 30, 2015

In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogen... more In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogeneity of the ordered structure of the Cauchy real numbers, and so this result holds in any topos with natural number object. However, it is well known that the real numbers objects obtained by the traditional constructions of Cauchy sequences and Dedekind cuts are not necessarily isomorphic in an arbitrary topos with natural numbers object. Consequently, Veldman and Waaldijk's result does not apply to the ordered structure of Dedekind real numbers in toposes. The main result to be proved in the present paper is that the ordered structure of the Dedekind real numbers object is homogeneous, in any topos with natural numbers object. This result is obtained within the framework of local set theory.

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Research paper thumbnail of A Paraconsistentist Approach to Chisholm's Paradox

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Research paper thumbnail of Modal Extensions of Sub-classical Logics for Recovering Classical Logic

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Research paper thumbnail of Finite non-deterministic semantics for some modal systems

Journal of Applied Non-Classical Logics, 2015

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Research paper thumbnail of Dugundji’s Theorem Revisited

Logica Universalis, 2014

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Research paper thumbnail of A Formal Framework for Hypersequent Calculi and their Fibring

The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, Volume I, Jan 1, 2015

Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suita... more Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between logics which preserves metaproperties in a strong sense. Finally, some preservation features are explored.

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Research paper thumbnail of Recovery operators, paraconsistency and duality

CLE e-Prints, 2017

There are two foundational but not properly developed ideas in da Costa's approach to paraconsist... more There are two foundational but not properly developed ideas in da Costa's approach to paraconsistency: the 'well-behavedness' operator and the duality between paraconsistent and intuitionistic logics. The aim of this paper is to present how these two ideas can be developed by Logics of Formal Inconsistency (LFIs) and Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, and LFUs recover the validity of the excluded middle in a paracomplete scenario. We will present two formal systems, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core – in the case studied here, classical positive propositional logic (CPL+). mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. Then, we combine these two logics obtaining logics of formal inconsistency and undeterminedness (LFIUs), called mbCD and mbCDE. The swap structures semantics framework for LFIs, is adapted here for LFUs and LFIUs. This semantics allows us to prove the decidability of the proposed systems by means of finite non-deterministic matrices.

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Research paper thumbnail of Non-deterministic algebraization of logics by swap structures

arXiv:1708.08499 [math.LO], 2017

Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Ma... more Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Mathematics and in Computer Science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several logics of formal inconsistency (or LFIs) which cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multi-algebras in a suitable way. A decomposition theorem similar to Birkhoff's representation theorem is obtained for each class of swap structures. Moreover , when applied to the 3-valued algebraizable logic J3 the usual class of algebraic models is recovered, and the swap structures semantics became twist-structures semantics (as introduced by Fidel-Vakarelov). This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, which is closely connected with Kalman's functor, suggests that swap structures can be considered as non-deterministic twist structures, opening so interesting possibilities for dealing with non-algebraizable logics by means of multi-algebraic semantics.

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Research paper thumbnail of Relevant Information and Relevant Logic

In: Proceedings of the 6th "Dr. Antonio A. R. Monteiro" Congress of Mathematics, pp. 119-127. Bahia Blanca, Argentina, 2001. , 2001

In this paper we define and develop an algebraic structure associated with the concept of systems... more In this paper we define and develop an algebraic structure associated with the concept of systems of relevant information (SRI), which is a variant of the semilattice semantics proposed by A. Urquhart in [6]. The propositional relevant logic RP is introduced as the syntactical counterpart of the SRI-structures. This logic has a primitive-recursive decision procedure. The idea behind this logic is that of "Relevant Deduction" , in which each premise is a block of information relevant to the conclusion. Finally, we prove that the class of SRI-structures is a sound and complete semantics for the logic RP .

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Research paper thumbnail of On formal aspects of the epistemic approach to paraconsistency

This paper reviews the central points and presents some recent developments of the epistemic appr... more This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LETJ ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson's logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for both BLE and LETJ . The meanings of the connectives of BLE and LETJ , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A
formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LETJ is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed.

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Research paper thumbnail of Formal (In)consistency, Abduction and Modalities

Springer Handbook of Model-Based Science, 2017

This chapter proposes a study of philosophical and technical aspects of logics of formal inconsis... more This chapter proposes a study of philosophical and technical aspects of logics of formal inconsistency (LFI s), a family of paraconsistent logics that have resources to express the notion of consistency inside the object language. This proposal starts by presenting an epistemic approach to paraconsistency according to which the acceptance of a pair of contradictory propositions A and \(\neg A\) does not imply accepting both as true. It is also shown how LFIs may be connected to the problem of abduction by means of tableaux that indicate possible solutions for abductive problems. The connection between the notions of modalities and consistency is also worked out, and some LFIs based on positive modal logics (called anodic modal logics), are surveyed, as well as their extensions supplied with different degrees of negations (called cathodic modal logics). Finally, swap structures are explained as new and interesting semantics for the LFIs, and shown to be as a particular important case of the well-known possible-translations semantics (PTS ).

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Research paper thumbnail of Modal logic S4 as a paraconsistent logic with a topological semantics

Logic and Computation: Essays in Honour of Amilcar Sernadas, Jul 5, 2017

In this paper the propositional logic LTop is introduced, as an extension of classical propositio... more In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency.

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Research paper thumbnail of AGM-like paraconsistent belief change

Logic Journal of the IGPL, 2017

Two systems of belief change based on paraconsistent logics are introduced in this article by mea... more Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo, is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations.

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Research paper thumbnail of Errata and Addenda to ‘Finite non-deterministic semantics for some modal systems’

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly re... more In this note, an error in the axiomatization of Ivlev’s modal system Sa+
which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems” (CFP2015), is fixed. Additionally, some axioms proposed in (CFP2015) were slightly modified. All the technical results in (CFP2015) which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in (CFP2015) is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed.

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Research paper thumbnail of Towards an hyperalgebraic theory of non-algebraizable logics

CLE e-Prints, Vol. 16 N. 4, Oct 14, 2016

Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of L... more Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics of swap structures for LFIs, which are Nmatrices defined over triples in a Boolean algebra, generalizing Avron's semantics. In this paper we develop the first steps towards the possibility of defining an algebraic theory of swap structures for LFIs, by adapting concepts of universal algebra to multialgebras in a suitable way.

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Research paper thumbnail of Non-deterministic algebras and algebraization of logics

Filosofia da Linguagem e da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese), Dec 2015

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Research paper thumbnail of Contradictions in reasoning: an evil or a blessing?

The purpose of this short essay is to explain the role of contradictions in the development of sc... more The purpose of this short essay is to explain the role of contradictions in the development of scientific theories. We argue that contradictions are not to be seen as a signal of defeat, but overall as a chance for improvement.

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Research paper thumbnail of Paraconsistent Belief Revision based on a formal consistency operator

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both define... more In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not
necessarily related to the notion of formal consistency.

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Research paper thumbnail of Paraconsistent Belief Revision based on a formal consistency operator

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined... more In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency – not
necessarily related to the notion of formal consistency.

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Research paper thumbnail of On the set of intermediate logics between the truth and degree preserving Lukasiewicz logics

The aim of this paper is to explore the class of intermediate logics between the truth-preserving... more The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L ≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L ≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in [0, 1], but we show there are intermediate logics falling outside this family. Finally, we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A, F) such that A is a finite MV-algebra and F is a lattice filter.

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Research paper thumbnail of On the ordered Dedekind real numbers in toposes

Why is this a Proof? Festschrift for Luiz Carlos Pereira, Jun 30, 2015

In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogen... more In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogeneity of the ordered structure of the Cauchy real numbers, and so this result holds in any topos with natural number object. However, it is well known that the real numbers objects obtained by the traditional constructions of Cauchy sequences and Dedekind cuts are not necessarily isomorphic in an arbitrary topos with natural numbers object. Consequently, Veldman and Waaldijk's result does not apply to the ordered structure of Dedekind real numbers in toposes. The main result to be proved in the present paper is that the ordered structure of the Dedekind real numbers object is homogeneous, in any topos with natural numbers object. This result is obtained within the framework of local set theory.

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Research paper thumbnail of A Paraconsistentist Approach to Chisholm's Paradox

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Research paper thumbnail of Modal Extensions of Sub-classical Logics for Recovering Classical Logic

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Research paper thumbnail of Finite non-deterministic semantics for some modal systems

Journal of Applied Non-Classical Logics, 2015

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Research paper thumbnail of Dugundji’s Theorem Revisited

Logica Universalis, 2014

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Research paper thumbnail of A Formal Framework for Hypersequent Calculi and their Fibring

The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, Volume I, Jan 1, 2015

Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suita... more Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between logics which preserves metaproperties in a strong sense. Finally, some preservation features are explored.

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Research paper thumbnail of Filosofia da Linguagem e da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese)

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Research paper thumbnail of South American Journal of Logic

by John Corcoran, JY B, Marcelo Esteban Coniglio, Marcelo Coniglio, Eduardo Barrio, Amílcar Sernadas, Dirk Greimann, Radmila Jovanovic, Aldo Figallo Orellano, Ricardo Bianconi, Gustavo Pelaitay, and radmila jovanovic

South America is one of the 7 continents of the earth with many different countries and languages... more South America is one of the 7 continents of the earth with many different countries and languages. The SAJL will promote interaction among logicians based in South America and also between logicians from South America and logicians from other continents.
The aim of the South American Journal of Logic is to promote logic in all its aspects: philosophical, mathematical, computational, historical by publishing high quality peer-reviewed papers.
http://www.sa-logic.org/

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