Showing papers on "Paraconsistent logic published in 2017"
TL;DR: This paper argued that the disagreement is due to a difference in how the parties understand logic theories. But they also argued that logical pluralism is a plausible supplement to anti-exceptionalism.
Abstract: Logic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy (Proc Address Am Philos Assoc 76:61–90, 2002), Priest (Doubt truth to be a liar, OUP, Oxford, 2006a, The metaphysics of logic, CUP, Cambridge, 2014, Log et Anal, 2016), Russell (Philos Stud 171:161–175, 2014, J Philos Log 0:1–11, 2015), and Williamson (Modal logic as metaphysics, Oxford University Press, Oxford, 2013b, The relevance of the liar, OUP, Oxford, 2015). Although these authors agree on many methodological issues about logic, they disagree about which logic anti-exceptionalism supports. Williamson uses an anti-exceptionalist argument to defend classical logic, while Priest claims that his anti-exceptionalism supports nonclassical logic. This paper argues that the disagreement is due to a difference in how the parties understand logical theories. Once we reject Williamson’s deflationary account of logical theories, the argument for classical logic is undercut. Instead an alternative account of logical theories is offered, on which logical pluralism is a plausible supplement to anti-exceptionalism.
80 citations
TL;DR: It is argued that the logic of requirements is exactly what the authors need in order to make sense of, and buttress, a constructionist (poietic) approach to knowledge.
Abstract: In this article, I outline a logic of design of a system as a specific kind of conceptual logic of the design of the model of a system, that is, the blueprint that provides information about the system to be created. In section two, I introduce the method of levels of abstraction as a modelling tool borrowed from computer science. In section three, I use this method to clarify two main conceptual logics of information (i.e., modelling systems) inherited from modernity: Kant's transcendental logic of conditions of possibility of a system, and Hegel's dialectical logic of conditions of in/stability of a system. Both conceptual logics of information analyse structural properties of given systems. Strictly speaking, neither is a conceptual logic of information about (or modelling) the conditions of feasibility of a system, that is, neither is a logic of information as a logic of design. So, in section four, I outline this third conceptual logic of information and then interpret the conceptual logic of design as a logic of requirements, by introducing the relation of "sufficientisation". In the conclusion, I argue that the logic of requirements is exactly what we need in order to make sense of, and buttress, a constructionist (poietic) approach to knowledge.
44 citations
TL;DR: The aim of the present essay is to investigate Stragey 1, an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented.
Abstract: A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes.
34 citations
TL;DR: A modal logic, KX4, in which $$\square X$$□X can be read as asserting there is implicit evidence for X, where the authors understand evidence to permit contradictions in a formal sense, is introduced, and BLE is shown to be equivalent to Nelson's paraconsistent logic N4.
Abstract: In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence (BLE) whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which $$\square X$$
can be read as asserting there is implicit evidence for X, where we understand evidence to permit contradictions. We show BLE embeds into KX4 in the same way that Intuitionistic logic embeds into S4. Then we formulate a new justification logic, JX4, in which the implicit evidence motivating KX4 is made explicit. KX4 embeds into JX4 via a realization theorem. Thus BLE has both implicit and explicit possibly contradictory evidence interpretations in a formal sense.
28 citations
TL;DR: The authors argue that logic is not normative and distinguish three different ways in which a theory can be entangled with the normative, and they show how logic is only entangled in the weakest of these ways, one which requires it to have no normativity of its own.
Abstract: Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and how we ought to reason, so that pluralism about the consequence relation would result in an incoherent or unattractive pluralism about those things. In this paper I argue that logic isn’t normative. I distinguish three different ways in which a theory – such as a logical theory – can be entangled with the normative and argue that logic is only entangled in the weakest of these ways, one which requires it to have no normativity of its own. I use this view to show what is wrong with three different arguments for the conclusion that logic is normative.
25 citations
TL;DR: This paper identifies a small set of properties that are instantiated in those various consequence relations, namely truth-relationality, valuemonotonicity, validity-coherence, and a constraint of bivalence-compliance, provably replaceable by a structural requisite of non-triviality.
Abstract: Several definitions of logical consequence have been proposed in many-valued logic, which coincide in the two-valued case, but come apart as soon as three truth values come into play. Those definitions include so-called pure consequence, order-theoretic consequence, and mixed consequence. In this paper, we examine whether those definitions together carve out a natural class of consequence relations. We respond positively by identifying a small set of properties that we see instantiated in those various consequence relations, namely truth-relationality, valuemonotonicity, validity-coherence, and a constraint of bivalence-compliance, provably replaceable by a structural requisite of non-triviality. Our main result is that the class of consequence relations satisfying those properties coincides exactly with the class of mixed consequence relations and their intersections, including pure consequence relations and order-theoretic consequence. We provide an enumeration of the set of those relations in finite many-valued logics of two extreme kinds: those in which truth values are well-ordered and those in which values between 0 and 1 are incomparable.
25 citations
TL;DR: The cut-elimination theorem is proved for a version of controlled propositional classical logic, i.e. the sequent calculus for classical propositional logic to which a suitable system of control sets is applied.
Abstract: The goal of this article is to design a uniform proof-theoretical framework encompassing classical, non-monotonic and paraconsistent logic. This framework is obtained by the control sets logical device, a syntactical apparatus for controlling derivations. A basic feature of control sets is that of leaving the underlying syntax of a proof system unchanged, while affecting the very combinatorial structure of sequents and proofs. We prove the cut-elimination theorem for a version of controlled propositional classical logic, i.e. the sequent calculus for classical propositional logic to which a suitable system of control sets is applied. Finally, we outline the skeleton of a new (positive) account of non-monotonicity and paraconsistency in terms of concurrent processes.
18 citations
TL;DR: Theorems for syntactically and semantically embedding CP into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved and several versions of Glivenko and Gödel-Gentzen translation theorems are proved for CP and IP.
Abstract: A classical paraconsistent logic (CP), which is regarded as a modified extension of first-degree entailment logic, is introduced as a Gentzen-type sequent calculus This logic can simulate the classical negation in classical logic by paraconsistent double negation in CP Theorems for syntactically and semantically embedding CP into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved The cut-elimination and completeness theorems for CP are also shown using these embedding theorems Similar results are also obtained for an intuitionistic paraconsistent logic (IP), and several versions of Glivenko and Godel-Gentzen translation theorems are proved for CP and IP
15 citations
TL;DR: There is exactly one self-extensional three-valued paraconsistent logic in the language of ¬,∧,∨} for which ∨ is a disjunction, and∧ is a conjunction, and this paper investigates the main properties of this logic, determines the expressive power of its language, and provides a cut-free Gentzen-type proof system for it.
Abstract: A logic $$\mathbf{L}$$
is called self-extensional if it allows to replace occurrences of a formula by occurrences of an $$\mathbf{L}$$
-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, there is exactly one self-extensional three-valued paraconsistent logic in the language of $$\{\lnot ,\wedge ,\vee \}$$
for which $$\vee $$
is a disjunction, and $$\wedge $$
is a conjunction. We also investigate the main properties of this logic, determine the expressive power of its language (in the three-valued context), and provide a cut-free Gentzen-type proof system for it.
12 citations
TL;DR: Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved.
Abstract: Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.
11 citations
01 Jan 2017
TL;DR: The notion of logical containment was introduced by Parry as mentioned in this paper in his system of analytic implication AI, which was later expanded to the system PAI. The hallmark of Parry's systems, and of what may be thought of as containment logics or Parry systems in general, is a strong relevance property called the "Proscriptive Principle" (PP), described as the thesis that: No formula with analytic implication as main relation holds universally if it has a free variable occurring in the consequent but not the antecedent.
Abstract: The Proscriptive Principle and Logics of Analytic Implication by Thomas Macaulay Ferguson Adviser: Professor Graham Priest The analogy between inference and mereological containment goes at least back to Aristotle, whose discussion in the Prior Analytics motivates the validity of the syllogism by way of talk of parts and wholes. On this picture, the application of syllogistic is merely the analysis of concepts, a term that presupposes—through the root ἀνά + λύω —a mereological background. In the 1930s, such considerations led William T. Parry to attempt to codify this notion of logical containment in his system of analytic implication AI. Parry’s system AI was later expanded to the system PAI. The hallmark of Parry’s systems—and of what may be thought of as containment logics or Parry systems in general—is a strong relevance property called the ‘Proscriptive Principle’ (PP) described by Parry as the thesis that: No formula with analytic implication as main relation holds universally if it has a free variable occurring in the consequent but not the antecedent. This type of proscription is on its face justified, as the presence of a novel parameter in the consequent corresponds to the introduction of new subject matter. The plausibility of the thesis that the content of a statement is related to its subject matter thus appears also to support the validity of the formal principle. Primarily due to the perception that Parry’s formal systems were intended to accurately model Kant’s notion of an analytic judgment, Parry’s deductive systems—and the suitability
11 Sep 2017
TL;DR: The cut-elimination theorem for FBD+ is shown and the completeness theorems with respect to both valuation and many-valued semantics forFBD+ are proved.
Abstract: In this paper, we investigate an extended first-order Belnap-Dunn logic with classical negation. We introduce a Gentzen-type sequent calculus FBD+ for this logic and prove theorems for syntactically and semantically embedding FBD+ into a Gentzen-type sequent calculus for first-order classical logic. Moreover, we show the cut-elimination theorem for FBD+ and prove the completeness theorems with respect to both valuation and many-valued semantics for FBD+.
TL;DR: It is proved that there exist only four logics that have the property of not satisfying any of the formulations of the principle of non contradiction, and among the three-valued logics, which of these logics satisfy this property.
Abstract: The authors of Beziau and Franceschetto (New directions in paraconsistent logic, vol 152, Springer, New Delhi, 2015) work with logics that have the property of not satisfying any of the formulations of the principle of non contradiction, Beziau and Franceschetto also analyze, among the three-valued logics, which of these logics satisfy this property. They prove that there exist only four of such logics, but only two of them are worthwhile to study. The language of these logics does not consider implication as a connective. However, the enrichment of a language with an implication connective leads us to more interesting systems, therefore we look for one implication for these logics and we study further properties that the logics obtain when this connective is added to these systems.
TL;DR: The present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM, and representation theorems w.r.t. constructions based on selection functions are obtained for all the operations.
Abstract: Two systems of belief change based on paraconsistent logics are introduced in this paper by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic that extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGM◦, is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator which 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.
01 Jan 2017
TL;DR: It is shown how to use the proof assistant Isabelle to formally prove theorems in the logic as well as meta-theorems about the logic, which has a countably infinite number of non-classical truth values.
Abstract: We present a formalization of a so-called paraconsistent logic that avoids the catastrophic explosiveness of inconsistency in classical logic. The paraconsistent logic has a countably infinite number of non-classical truth values. We show how to use the proof assistant Isabelle to formally prove theorems in the logic as well as meta-theorems about the logic. In particular, we formalize a meta-theorem that allows us to reduce the infinite number of truth values to a finite number of truth values, for a given formula, and we use this result in a formalization of a small case study.
01 May 2017
TL;DR: Theorems for syntactically and semantically embedding PL into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved and the cut-elimination and completeness theorem for PL are obtained via these embedding theorems.
Abstract: We introduce a Gentzen-type sequent calculus PL for a modified extension of Arieli, Avron and Zamansky's ideal paraconsistent four-valued logic 4CC. The calculus PL, which is also regarded as a paradefinite four-valued logic, is formalized based on the idea of connexive logic. Theorems for syntactically and semantically embedding PL into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for PL are obtained via these embedding theorems. Moreover, we introduce an extension EPL of both PL and a Gentzen-type sequent calculus for 4CC, and show the cut-elimination theorem for EPL. The calculus EPL has a novel characteristic property of negative symmetry.
13 Oct 2017
TL;DR: In this article, the authors focus on two main families of unifying approaches based on two different ways to conceive logic: 1) the traditional conception of logic, according to which a logical systems is determined by the set of inferential rules. 2) the formal semantics conception, which proposes to unify logical systems by studying them under the background of the kind of truth-functional semantics presupposed by the determination of their valid formulae.
Abstract: About 40 years ago, or perhaps even earlier, logical systems started to emerge at a breath-taking pace almost every day. At the same time several unifying approaches have been proposed, that are also plural. Let me focus on two main families of unifying approaches based on two different ways to conceive Logic: 1. One approach takes up the traditional conception of logic, according to which a logical systems is determined by the set of inferential rules. 2. The other main approach that appeared around the 60ties, conceives logical systems as the set of valid formulae they determine. Thus, according to the first approach, let us call it the inferentialist conception, we can unify different logical systems by changing some rules or properties of the inference relation. A common example is to distinguish classical logic from intuitionistic logic by distinguishing between a logical systems that allows more than one conclusion (classical logic) and one that do not (intuitionistic logic). In relation to the second approach, let me call it the formal semantics conception, proposes to unify logical systems by studying them under the background of the kind of truth-functional semantics presupposed by the determination of their valid formulae. For example, some early attempts to distinguish classical logic from intuitionistic logic, was to compare these logics by comparing them under the background of a truth-functional semantics. According to these perspective while classical logic is the set of valid formulae determined by Boolean-truth functions, the valid formulae of intuitionistic logic are determined by some specific form of a three-valued truth-function: so while the third excluded is valid under the Boolean background it is not valid under the three-valued one. Moreover, while the formal semantics approach is built on the traditional strict differentiation between semantics, syntax and pragmatics inherited from Charles Morris (1938, p.3) – that I may recall was published in the first volume of the International Encylcopedia of Unified Science, inferentialism grew up out of a background that avoids keeping form and meaning apart (see Martin-Lof (1984, p. 2)), and the dialogical form of inferentialism, main subject of 1 The paper has been developed in the context of the researches for transversal research axis Argumentation (UMR 8163: STL), the research project ADA at the MESHS-Nord-pas-de-Calais and the research projects: ANR-SEMAINO (UMR 8163: STL).
TL;DR: In this paper, the authors present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways: it includes an account of Wittgenstein's "form-series" device, which suffices to express some effectively generated countably infinite disjunctions.
Abstract: I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably infinite, then the property of being a tautology is -complete. But third, it is only granted the assumption of countability that the class of tautologies is -definable in set theory. Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects.
23 Feb 2017
TL;DR: In this article, the relation to the object that decides, as in the case of logic, which algebra is to be used is discussed, and two probabilistic algebras are proposed: one for classical probability and the other for quantum mechanics.
Abstract: There are two probabilistic algebras: one for classical probability and the other for quantum mechanics. Naturally, it is the relation to the object that decides, as in the case of logic, which algebra is to be used. From a paraconsistent multivalued logic therefore, one can derive a probability theory, adding the correspondence between truth value and fortuity.
TL;DR: In this article, the authors present two logics that characterize the formulas that defy excluded middle while maintaining that not all formulas are of this kind, while still maintaining that there are some formulas that obey explosion.
Abstract: This paper contributes to the study of paracompleteness and paraconsistency. We present two logics that address the following questions in novel ways. How can the paracomplete theorist characterize the formulas that defy excluded middle while maintaining that not all formulas are of this kind? How can the paraconsistent theorist characterize the formulas that obey explosion while still maintaining that there are some formulas not of this kind?
01 Jan 2017
TL;DR: In this paper, the authors examine up to which point Modern logic can be qualified as non-Aristotelian and compare it with propositional and first-order logic.
Abstract: In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare syllogistic with propositional and first-order logic. We touch the question of formal validity, variable and mathematization and we point out that Gentzen’s cut-elimination theorem can be seen as the rejection of the central mechanism of syllogistic – the cut-rule having been first conceived as a modus Barbara by Hertz. We then examine the non-Aristotelian aspect of some non-classical logics, in particular paraconsistent logic. We argue that a paraconsistent negation can be seen as neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’ square of opposition. We end by examining if the comparison promoted by Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes sense.
Journal Article•
TL;DR: Chunk and permeate is examined, a simple approach to paraconsistent reasoning which avoids heterodox logic by confining commitments to separate contexts in which reasoning with them is taken to be reliable while allowing ‘permeation’ of some conclusions into other contexts, can help to systematize pluralistic reasoning across the boundaries of plural contexts.
Abstract: Scientific inquiry is typically focused on particular questions about particular objects and properties. This leads to a multiplicity of models which, even when they draw on a single, consistent body of concepts and principles, often employ different methods and assumptions to model different systems. Pluralists have remarked on how scientists draw on different assumptions to model different systems, different aspects of systems and systems under different conditions and defended the value of distinct, incompatible models within science at any given time. (Cartwright, 1999; Chang, 2012) Paraconsistentists have proposed logical strategies to avoid trivialization when inconsistencies arise by a variety of means.(Batens, 2001; Brown, 1990; Brown, 2002) Here we examine how chunk and permeate, a simple approach to paraconsistent reasoning which avoids heterodox logic by confining commitments to separate contexts in which reasoning with them is taken to be reliable while allowing ‘permeation’ of some conclusions into other contexts, can help to systematize pluralistic reasoning across the boundaries of plural contexts, using regional climate models as an example.(Benham et al., 2014; Brown & Priest 2004, 2015) The result is a kind of unity for science—but a unity achieved by the constrained exchange of specified information between different contexts, rather than the closure of all commitments under some paraconsistent consequence relation.
11 Sep 2017
TL;DR: The aim of this paper is to fill in the gap by presenting a semantics for P \(^1\) a la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic.
Abstract: One of the simple approaches to paraconsistent logic is in terms of three-valued logics. Assuming the standard behavior with respect to the “classical"values, there are only two possibilities for paraconsistent negation, namely the negation of the Logic of Paradox and the negation of Sette’s logic P \(^1\). From a philosophical perspective, the paraconsistent negation of P \(^1\) is less discussed due to the lack of an intuitive reading of the third value. Based on these, the aim of this paper is to fill in the gap by presenting a semantics for P \(^1\) a la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic. A variant of P \(^1\) known as I \(^1\) will be also discussed.
TL;DR: The algebraic and combinatorial structure of negation in a non-commutative variant of tensorial logic is studied, based on a 2-categorical account of dialogue categories, which unifies Tensorial logic with linear logic, and discloses a primitive symmetry between proofs and anti-proofs.
TL;DR: The authors argue that Steinberger's criticisms fail for one such formulation and sketch an argument, available to those who deny dialetheism, in defence of the formulation in question, which is available to all paraconsistent logics.
Abstract: One strategy for defending paraconsistent logics involves raising ‘normative arguments’ against the inference rule explosion. Florian Steinberger systematically criticises a wide variety of formulations of such arguments. I argue that, for one such formulation, Steinberger's criticisms fail. I then sketch an argument, available to those who deny dialetheism, in defence of the formulation in question.
01 Jan 2017
TL;DR: This paper explores some potential means of defining consistency and negation when expressed in modal terms, and takes some first steps in exploring the philosophical significance of such logical tools in the family of Logics of Formal Inconsistency (LFIs), suggesting some experiments on their expressive power.
Abstract: This paper discusses logical accounts of the notions of consistency and negation, and in particular explores some potential means of defining consistency and negation when expressed in modal terms. Although this can be done with interesting consequences when starting from classical normal modal logics, some intriguing cases arise when starting from paraconsistent modalities and negations, as in the hierarchy of the so-called cathodic modal paraconsistent systems (cf. Bueno-Soler, Log Univers 4(1):137–160, 2010). The paper also takes some first steps in exploring the philosophical significance of such logical tools, comparing the notions of consistency and negation modally defined with the primitive notions of consistency and negation in the family of Logics of Formal Inconsistency (LFIs), suggesting some experiments on their expressive power.
26 Jun 2017
TL;DR: This paper introduces \(\text {4QL}^{\!\text {Bel}\), a four-valued rule language designed for reasoning with paraconsistent and paracomplete belief bases as well as belief structures.
Abstract: This paper introduces \(\text {4QL}^{\!\text {Bel}}\), a four-valued rule language designed for reasoning with paraconsistent and paracomplete belief bases as well as belief structures. Belief bases consist of finite sets of ground literals providing (partial and possibly inconsistent) complementary or alternative views of the world. As introduced earlier, belief structures consist of constituents, epistemic profiles and consequents. Constituents and consequents are belief bases playing different roles. Agents perceive the world forming their constituents, which are further transformed into consequents via the agents’ or groups’ epistemic profile.
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TL;DR: This work describes the happening of the 1st World Congress on Logic and Religion and explains the motivation for developing the interaction between logic and religion.
Abstract: We first start by describing the happening of the 1st World Congress on Logic and Religion. We then explain the motivation for developing the interaction between logic and religion. In a third part we discuss some papers presented at this event published in the present special issue.
01 Jan 2017
TL;DR: 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.
Abstract: 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 \(
eg A\) 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 ).
01 May 2017
TL;DR: The exclusion problem concerning the classes of involutive bounded lattices, logics, and quantum logics (i.e., orthomodular lattices), and it is obtained that a logic is a quantum logic if and only if it is a paraconsistent logic.
Abstract: In this paper, we study the exclusion problem concerning the classes of involutive bounded lattices, logics, and quantum logics (i.e., orthomodular lattices). We also obtain that a logic is a quantum logic if and only if it is a paraconsistent logic. Moreover, we give some considerations on an open question to find sufficient conditions for the existence of an orthomodular orthocomplementation on lattices. Furthermore, we revisit the Dedekind---MacNeille completion of involutive bounded posets and correct a widely cited error in quantum logics.