Proceedings of the II World Congress on Paraconsistency held in Juquey, SP, Brazil, from May 12-19, 2000.

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”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in 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. (shrink)

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, (...) syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS''s). This generalization allows us to define BRS''s in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers. (shrink)

The ``Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the State University (...) of Campinas (UNICAMP) XV EBL -15th Brazilian Logic Conference XIV SLALM - 14th Latin-American Symposium on Mathematical Logic Several renowned logicians, philosophers and mathematicians gathered in colonial Paraty, a historic village on the Brazilian coast founded in the 17th Century and surrounded by the luscious Atlantic rain forest to deliver lectures and talks celebrating the many sides of logic: the philosophical, the mathematical, the computational, the historical, and the multiple facets therein. The topics of the joint conferences, well represented here, included philosophical and mathematical Logic and applications with emphasis on model theory and proof theory, set theory, non-classical logics and applications, history and philosophy of logic, philosophy of the formal sciences and issues on the foundations of mathematics. The events have been preceded by a Logic School planned for students and young researchers held at the UNICAMP campus in Campinas, SP. (shrink)

This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows from _A_’s violating some classically valid inferences. The semantics of _Q__L__E__T_ (...) _F_ combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of _FDE_, _K3_, and _LP_, we show how these tools, which we call here the method of _anti-extensions + valuations_, can be naturally applied to a number of non-classical logics. (shrink)

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...) result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of the paper (...) is devoted to four-valued Nmatrices, including Kearns’s and Ivlev’s. Besides proving with full details Kearns’s results for T, S4 and S5, we also obtain a characterisation of the system B by four-valued Nmatrices with level valuations. Concerning Ivlev’s results, two new modal systems are introduced and char.. (shrink)

In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal logic (...) can be characterized by Kripke frames. Besides, the creation of non-classical modal logics puts the problem of characterization of finite matrices very far away from the original scope of Dugundji’s result. In this sense, we will show how to update Dugundji’s result in order to make precise the scope and the limits of many-valued matrices as semantic of modal systems. A brief comparison with the useful Chagrov and Zakharyaschev’s criterion of tabularity for modal logics is provided. (shrink)

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. (shrink)

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to (...) recover the theorems of propositional classical logic within three sub-classical modal systems. (shrink)

After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.

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. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to many-valued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called Pn and a hierarchy (...) of paracomplete logics In. We also propose three further generalizations, obtaining Society Semantics for several many-valued logics, including a hierarchy of logics called In Pk which are both paraconsistent and paracomplete. (shrink)

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 (LET J ), 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 LET J . The meanings of the connectives of BLE and LET J , 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 LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...) approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)

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. (shrink)

Tetravalent modal logic (TML) was introduced by Font and Rius in 2000. It is an expansion of the Belnap-Dunn four-valued logic FOUR, a logical system that is well-known for the many applications found in several fields. Besides, TML is the logic that preserves degrees of truth with respect to Monteiro’s tetravalent modal algebras. Among other things, Font and Rius showed that TML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in a (...) previous work we presented a sequent system for TML with the cut-elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present article we continue with the study of TML under a proof-theoretic perspective. In the first place, we show that the natural deduction system that we introduced before admits a normalization theorem. In the second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced by A. V. Figallo and P. Landini, we define a decidable tableau system adequate to check validity in the logic TML. Finally, we provide a sound and complete tableau system for TML in the original language. These two tableau systems constitute new (proof-theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras. (shrink)

In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...) analyze the class of mbC-structures. Thus, substructures, union of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect poducts in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for Cn-structures. (shrink)

In this paper we develop the elementary theory of modules in the category Sh of sheaves over right-sided idempotent quantales. The main ingredient is the construction of a logic sound for Sh . As an application we prove that in Sh , a finitely generated projective module is free , a result that is relevant to the study of representation of non-commutative C ∗ -algebras.

In spite of his post-World War II works on international law, which seems more purely juridical, Hans Kelsen continues to put forward in his vast body of work an implicit – and sometimes even explicit – juridical objectivism and pacifism. Especially before and during the second World War he makes – by means of many moral-political writings – an effort for a more effective assurance of international peace. The fact that Kelsen regards the law as the pre-eminent means to achieve (...) the end of peace, is – in view of the tradition running from Hobbes to Kant – still not very innovating. But the primary and central role he assigns to the judiciary in order to guarantee international peace is on the other hand really original. To bring out Kelsen’s juridical objectivism and pacifism, I restrict myself in this article to his plea before and during the second World War for the judicial primacy in the international legal order. In that plea, which is spread over many writings and founded by several arguments, I distinguish however three main convincing arguments – namely an evolutionary, a technical and a moral-political argument – for the establishment of an international court with compulsory jurisdiction as the ‘guardian of international peace’. The fact that Kelsen’s original plea is still relevant to our times, is already evident from the post-World War II UN-system of peace-enforcement, which still functions little satisfactorily and of which the existing plans of reform go no further than strengthening the position of the Security Council, the current hardly effective ‘maintainer of world peace’. (shrink)

The Oxford Handbook of Feminist Theory provides an overview of the analytical frameworks and theoretical concepts feminist theorists have developed to challenge established knowledge. Leading feminist theorists, from around the globe, provide in-depth explorations of a diverse array of subject areas, capturing a plurality of approaches. The Handbook raises new questions, brings new evidence, and poses significant challenges across the spectrum of academic disciplines, demonstrating the interdisciplinary nature of feminist theory.

The relevance of the research is the intensity of noise emitted by lorries depends on the regime of the vehicle movement. One of the main negative factors caused by road vehicles is air pollution with exhaust gases. The article presents results for noise caused by lorries and gas usage while the vehicle is accelerating. The subject of the study is 4 lorries, and they also feature fuel recording systems which are less than 5 years old. Research methodology. The level of (...) noise emitted by heavyweight transport vehicles is measured according to Lithuanian standard LST ISO 1996-2:2008 requirements. During the tests the noise levels of L A,eq, L C,eq, L C,peak were measured. The tests were done 5 times each and the results are presented as arithmetical averages. Fuel consumption is registered in vehicle data registration system. The researched vehicles have to comply with environmental safety normative requirements; that the vehicle carbon monoxide, particulate matter, nitrogen oxides, unburned fuel and other hazardous substances contained in the combustion gases must not exceed the prescribed limits. The results of the experimental studies show that EURO6 lorries noise level is the lowest compared to the EURO4 and EURO5. After carrying out the analysis of the caused noise and gas usage, it was found that noise pollution and gas usage are higher without speed control system. The noise caused by lorries can be described in square polynomial which defines the noise inclination change while vehicle is accelerating. Scientific novelty of the research a complex research on noise and fuel consumption of lorries by using and not using speed control system. Research idea and problem is to achieve sustainable transport development objectives, in particular the reduction of greenhouse gas emissions under the Kyoto Protocol. It is very important to find ways to forecast and reduce transport noise pollution, while also reducing overall pollution, as well as mitigating the impact on the global climate., Conclusion – after conducting a lorry noise and fuel consumption analysis, it was determined that not using speed control system increases the noise and fuel consumption and if the system is used both of these factors decrease drastically. (shrink)

Synaesthesia is a condition in which one type of stimulation evokes the sensation of another, as when the hearing of a sound produces photisms, i.e. mental percepts of colours. R is a 20 year old colour blind subject who, in addition to the relatively common grapheme-colour synaesthesia, presents a rarely reported cross modal perception in which a variety of visual stimuli elicit aura-like percepts of colour. In R, photisms seem to be closely related to the affective valence of stimuli and (...) typically bring out a consistent pattern of emotional responses. The present case study suggests that colours might be an intrinsic category of the human brain. We developed an empirical methodology that allowed us to study the subject's otherwise inaccessible phenomenological experience. First, we found that R shows a Stroop effect elicited by photisms despite the fact that he does not show a regular Stroop with real colours. Secondly, by manipulating the colour context we confirmed that colours can alter R's emotional evaluation of the stimuli. Furthermore, we demonstrated that R's auras may actually lead to a partially inverted emotional spectrum where certain stimuli bring out emotional reactions opposite to the normal ones. These findings can only be accounted for by considering R's subjective colour experience or qualia. Therefore the present paper defends the view that qualia are a useful scientific concept that can be approached and studied by experimental methods. (shrink)

PURPOSE: To evaluate the effects of social support on comprehension and recall of consent form information in a study of Parkinson disease patients and their caregivers.DESIGN and METHODS: Comparison of comprehension and recall outcomes among participants who read and signed the consent form accompanied by a family member/friend versus those of participants who read and signed the consent form unaccompanied. Comprehension and recall of consent form information were measured at one week and one month respectively, using Part A of the (...) Quality of Informed Consent Questionnaire .RESULTS: The mean age of the sample of 143 participants was 71 years . Analysis of covariance was used to compare QuIC scores between the intervention group and control group . In the 1-week model, no statistically significant intervention effect was found . However, the intervention status by patient status interaction was statistically significant . In the 1-month model, no statistically significant intervention effect was found . Again, however, the intervention status by patient status interaction was statistically significant . At both time periods, intervention group patients scored higher on the QuIC than did intervention group caregivers, and control group patients scored lower on the QuIC than did control group caregivers.IMPLICATIONS: Social support played a significant role in enhancing comprehension and recall of consent form information among patients. (shrink)

Provability, Computability and Reflection.

The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

IntroductionAt present, in the UK, live lobe donation of the lung is generally considered in the context of patients with cystic fibrosis which is a life-threatening, inherited disease.1 However, if this technique is successfully developed it may be applicable to other patients with end stage lung disease. Cystic fibrosis is a disease where the major morbidity and mortality is due to pulmonary infection and respiratory failure.2 In l938 70% of patients born with CF died within one year of birth, but (...) now the average survival has improved to 32 years.1 The improved survival has been due to improved medical care, but also, and in very large measure, to the devotion of the families who have carried out time-consuming daily treatments such as chest physiotherapy, nebuliser treatment, high calorie diets etc. To these patients and their families lung transplantation brought new hope.3 The first successful transplant for CF was performed in the UK in 1985 and we now have patients alive and well more than ten years after transplantation. However, sadly, nearly 50% of patients with CF die on the transplant waiting list because of a shortage of donor organs from brain stem dead donors. This is a tragedy for the individual patient, the families and those who care for them. Is there a way forward?Can the number of organs available for transplantation be increased?Education of the public so that a relative of a brain dead individual will give permission for the organs to be used has been carried out for many years but only with a small increase in the number of available organs. “Required request” where doctors would be required, by law, to ask relatives of brain dead patients to consider transplantation and “assume consent” where consent to donation is assumed unless there is evidence to the contrary, do not have the …. (shrink)

This article examines the (bio) ethical and professionalism issues that may arise in the context of medical practice in low and middle income countries (LAMIC), and the challenges this poses for medical regulatory bodies in the regions, in upholding ethics in professional practice. A quadrangle of source of the problems given rise to the breach of ethics in medical practice is identified, and suggested steps, based on ethical principles and concept, is proposed towards the resolution of the problems presented. As (...) LAMIC progress to improve the health of its population, this endeavour should occur hand in hand with contemporary medical ethics theories, taking in context the region’s ethnographic and cultural beliefs and practices. (shrink)

In their “social contextual view” of emotional mimicry, authors Hess and Fischer (2022) put forward emotional mimicry as a social regulator, considering it a social act, bound to certain affiliative contexts or goals. In this commentary, we argue that the core function of mimicry is to ease predicting conspecifics’ behaviours and the environment, and that as a consequence, this often smoothens social interactions. Accordingly, we make three main points. First, we argue that there is no good reason to believe that (...) the mimicry of negative expressions is fundamentally different than the mimicry of positive or ambiguous or autonomic expressions. Second, we give examples of empirical evidence that mimicry is not always a social act. Third, we show that mimicry has primary benefits for the mimicker. As such, we will briefly summarise and elaborate on the relevant findings in these respects, and propose a comparative, multi-method and ecologically valid approach which can explain the multifaceted character of the phenomenon. (shrink)