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)

It is well-known that da Costa's C-systems of paraconsistent logic do not admit a Blok-Pigozzi algebraization. Still, an algebraic flavored semantics for them has been proposed in the literature, namely using the class of so-called da Costa algebras. However, the precise connection between these semantic structures and the C-systems was never established at the light of the theory of algebraizable logics. In this paper we propose to study the C-systems from an algebraic point of view, and to fill in this (...) gap by using the tools and techniques of the newly developed behavioral approach to abstract algebraic logic. As a by-product of the approach, we also rediscover the bivaluation semantics of the logics. (shrink)

Two famous negative results about da Costa’s paraconsistent logic ${\mathscr {C}}_1$ (the failure of the Lindenbaum–Tarski process [44] and its non-algebraizability [39]) have placed ${\mathscr {C}}_1$ seemingly as an exception to the scope of Abstract Algebraic Logic (AAL). In this paper we undertake a thorough AAL study of da Costa’s logic ${\mathscr {C}}_1$. On the one hand, we strengthen the negative results about ${\mathscr {C}}_1$ by proving that it does not admit any algebraic semantics whatsoever in the sense of Blok (...) and Pigozzi (a weaker notion than algebraizability also introduced in the monograph [6]). On the other hand, ${\mathscr {C}}_1$ is a protoalgebraic logic satisfying a Deduction-Detachment Theorem (DDT). We then extend our AAL study to some paraconsistent axiomatic extensions of ${\mathscr {C}}_1$ covered in the literature. We prove that for extensions ${\mathcal {S}}$ such as ${\mathcal {C}ilo}$ [26], every algebra in ${\mathsf {Alg}}^*({\mathcal {S}})$ contains a Boolean subalgebra, and for extensions ${\mathcal {S}}$ such as,, or [16, 53], every subdirectly irreducible algebra in ${\mathsf {Alg}}^*({\mathcal {S}})$ has cardinality at most 3. We also characterize the quasivariety ${\mathsf {Alg}}^*({\mathcal {S}})$ and the intrinsic variety $\mathbb {V}({\mathcal {S}})$, with,, and. (shrink)

Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also introduced. In this alternative (...) procedure hidden variables are also used, but in this case to represent the degree of true or falsehood of propositions. (shrink)

We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics, whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics (...) of strengthening a given many-valued logic with additional axioms, the study of conditions under which a given logic may be seen as a combination of simpler syntactically defined fragments whose calculi can be obtained independently and put together to form a calculus for the whole logic, and also general conditions for decidability to be preserved by the combination mechanism. (shrink)

De Interpretatione is among Aristotle's most influential and widely read writings; C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system. He shows that De Interpretatione is not a disjointed essay on ill-connected subjects, as traditionally thought, but a highly organized and systematic treatise on logic, argument, and dialectic.

The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by (...) allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper. (shrink)

The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more (...) than two values? Because, we argue, one has to decide how to deal with bivalence and settle down the tradeoff between logical 2-valuedness and truth-functionality, from a pragmatical standpoint. -/- This paper will illustrate the ups and downs of a two-valued reduction of logic. Suszko’s reductive result is quite non-constructive.We will exhibit here a way of effectively constructing the two-valued semantics of any logic that has a truth-functional finite-valued semantics and a sufficiently expressive language. From there, as we will indicate, one can easily go on to provide those logics with adequate canonical systems of sequents or tableaux. The algorithmic methods developed here can be generalized so as to apply to many non-finitely valued logics as well —or at least to those that admit of computable quasi tabular two-valued semantics, the so-called dyadic semantics. (shrink)

We discuss the axiomatization of generalized consequence relations determined by non-deterministic matrices. We show that, under reasonable expressiveness requirements, simple axiomatizations can always be obtained, using inference rules which can have more than one conclusion. Further, when the non-deterministic matrices are finite we obtain finite axiomatizations with a suitable generalized subformula property.

We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new (...) algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way toward a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several well-known characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach. (shrink)

Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction (...) systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequences systems. (shrink)

We study the general problem of strengthening the logic of a given matrix with a set of axioms, using the idea of rexpansion. We obtain two characterization methods: a very general but not very effective one, and then an effective method which only applies under certain restrictions on the given semantics and the shape of the axioms. We show that this second method covers a myriad of examples in the literature. Finally, we illustrate how to obtain analytic multiple-conclusion calculi for (...) the resulting logics. (shrink)

. The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. For (...) illustration, we revisit the example of combining intuitionistic and classical propositional logics. (shrink)

The authors present a case study involving truth telling responsibilities in the setting of nonepileptic seizures. Specifically, over the course of several suspected nonepileptic seizures, a patient’s seizures stopped after he received a saline flush meant to precede the administration of anti-seizure medication. The patient and his surrogate believed he had received the medication each time, and the team wondered whether they should disclose the truth. Some worried that disclosure would reinforce the suspected psychogenic behavior, exacerbating the patient’s condition. In (...) this way, the case study presents a twist on the traditional truth telling archetype. While most truth telling cases center on navigating cultural differences or worries about emotional harm, this case presented concerns about medical harm in the form of exacerbating the patient’s condition. The authors describe the complex patient-family-team dynamic that preceded this ethical dilemma, describe the case, analyze the ethical issue, and describe the outcome. (shrink)

The modern view of logical reasoning as modeled by a consequence operator has allowed for huge developments in the study of logic as an abstract discipline. Still, it is unable to explain why it is often the case that the same designation is used, in an ambiguous way, to describe several distinct modes of reasoning over the same logical language. A paradigmatic example of such a situation is ‘modal logic’, a terminology which can encompass reasoning over Kripke frames, but also (...) over Kripke models, and in any case either locally or globally . Herein, we adopt a novel abstract notion of logic presented as a lattice-structured hierarchy of consequence operators, and explore some common proof-theoretic and model-theoretic ways of presenting such hierarchies through a collection of meaningful examples. In order to illustrate the usefulness of the notion of hierarchical consequence operators we address a few questions in the theory of combined logics, where a suitable abstract presentation of the logics being combined is absolutely essential. We show how to define the operation, in general, and we achieve a number of interesting preservation results for fibring within the context of 2-hierarchies. (shrink)

We define and study abstract valuation semantics for logics, an algebraically well-behaved version of valuation semantics. Then, in the context of the behavioral approach to the algebraization of logics, we show, by means of meaningful bridge theorems and application examples, that abstract valuations are suited to play a role similar to the one played by logical matrices in the traditional approach to algebraization.

The Fregean-inspired Principle of Compositionality of Meaning for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the domain of (...) formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems. (shrink)

In previous work, we introduced a version of distributed temporal logic that is well-suited both for verifying security protocols and as a metalogic for reasoning about, and relating, different security protocol models. In this paper, we formally investigate the relationship between our approach and strand spaces, which is one of the most successful and widespread formalisms for analyzing security protocols. We define translations between models in our logic and strand-space models of security protocols, and we compare the results obtained with (...) respect to the level of abstraction that is inherent in each of the formalisms. This allows us to clarify different aspects of strand spaces that are often left implicit, as well as pave the way to transfer results, techniques and tools across the two approaches. (shrink)

We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations—nowadays more commonly called multiple-conclusion logics—to the setting of non-deterministic matrices (Nmatrices), characterizing the Nmatrix models of an arbitrary logic through a generalization of the standard class operators to the non-deterministic setting. We highlight the main differences that appear in this more general setting, in particular: the possibility to obtain Nmatrix quotients using any compatible equivalence relation (not necessarily a congruence); the (...) problem of determining when strict homomorphisms preserve the logic of a given Nmatrix; the fact that the operations of taking images and preimages cannot be swapped, which determines the exact sequence of operators that generates, from any complete semantics, the class of all Nmatrix models of a logic. Many results, on the other hand, generalize smoothly to the non-deterministic setting: we show for instance that a logic is finitely based if and only if both the class of its Nmatrix models and its complement are closed under ultraproducts. We conclude by mentioning possible developments in adapting the Abstract Algebraic Logic approach to logics induced by Nmatrices and the associated equational reasoning over non-deterministic algebras. (shrink)

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversedviews. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certainmathematical questions as internal questions appealing to logic and convention. On the contrary, Quine wasopposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of thispaper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlosimulations, limiting mathematical inquiry to the domain of (...) logic is unjustified. Robustness studies implemented inMonte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)

Postcolonial science studies entails ostensibly contradictory critical and empirical commitments. Science studies scholars influenced by Bruno Latour and Isabelle Stengers embrace forms of realist, radical empiricism, while postcolonial studies scholars influenced by Jacques Derrida trace the limits of the knowable. This essay takes their common use of the term cosmopolitics as an unexpected point of departure for reconciling Derrida’s program with Stengers’s and Latour’s. I read Derrida’s critique of hospitality and Stengers’s and Latour’s ontological politics as necessary complements for conceiving (...) a care-oriented subalternist cosmopolitics, a process of composing common worlds that remains attentive to the limits of representation. (shrink)

Do famous athletes have special obligations to act virtuously? A number of philosophers have investigated this question by examining whether famous athletes are subject to special role model obligations (Wellman 2003; Feezel 2005; Spurgin 2012). In this paper we will take a different approach and give a positive response to this question by arguing for the position that sport and gaming celebrities are ‘ambassadors of the game’: moral agents whose vocations as rule-followers have unique implications for their non-lusory lives. According (...) to this idea, the actions of a game’s players and other stakeholders—especially the actions of its stars—directly affect the value of the game itself, a fact which generates additional moral reasons to behave in a virtuous manner. We will begin by explaining the three main positions one may take with respect to the question: moral exceptionalism, moral generalism, and moral exemplarism. We will argue that no convincing case for moral exemplarism has thus far been made, which gives us reason to look for new ways to defend this position. We then provide our own ‘ambassadors of the game’ account and argue that it gives us good reason to think that sport and game celebrities are subject to special obligations to act virtuously. (shrink)

An examination of David Hume's philosophy of religion that situates his conception "true religion" within the context of his overall science of human nature, his rejection of popular religion, and his Ciceronian influence"--Provided by publisher.

We all experience loneliness at some time in our lives and it often motivates people, consciously or otherwise, to enter treatment. Yet it is rarely explicitly addressed in psychoanalytic literature. Loneliness and Longing rectifies this oversight by thoroughly exploring this painful psychological state. In this book contributors address the inner sense of loneliness âe" that is feeling alone even in the company of others âe" by drawing on different aspects of loneliness and longing. Topics covered include: loneliness in the consulting (...) room the relationship between loneliness and love the effects of social networking and the internet how loneliness changes throughout the life-cycle healing the analystâe(tm)s loneliness. Loneliness and Longing draws on both theory and practice to discuss ways to help people to understand and cope with this important emotional state, encouraging them to make loneliness and longing less pervasive in their lives. This will be ideal reading for analysts, psychotherapists, and related practitioners facing the challenges of loneliness in their consulting rooms. (shrink)

In ancient China, a revered Taoist sage named Zhuangzi told many parables. In Existential Psychology and the Way of the Tao, a selection of these parables will be featured. Following each parable, an eminent existential psychologist will share a personal and scholarly reflection on the meaning and relevance of the parable for psychotherapy and contemporary life. The major tenets of Zhuangzi's philosophy are featured. Taoist concepts of emptiness, stillness, Wu Wei (i.e. intentional non-intentionality), epistemology, dreams and the nature of reality, (...) character building in the midst of pain, meaning and the centrality of relationships, authenticity, self-care, the freedom that can come from one's willingness to confront death, spiritual freedom, and gradations of therapeutic care are topics highlighted in this book. (shrink)

Relative essentialism, the view that multiple objects about which there are distinct de re modal truths can occupy the same space at the same time, is a metaphysical view that dissolves a number of metaphysical issues. The present essay constructs and defends relative essentialism and argues that it is implicit in some of the ideas of W. V. Quine and Donald Davidson. Davidson’s published views about individuation and sameness can accommodate the common-sense insights about change and persistence of Aristotle and (...) Kripke. Aristotle and Kripke have to give up unmediated direct reference resting on a unique correct articulation of reality into entities. Davidson has to acknowledge a distinction between descriptions giving accidental and those giving essential features of an object. Quine and Davidson were in a position to be a relative essentialist, but were over-impressed by supervenience. The relative essentialist view of beings developed from Quine and Davidson strongly suggests the Heideggerian distinction between beings and Being, and is the perspective from which analytic philosophy can engage that topic. Relative essentialism also connects analytic philosophy to Derrida’s thinking about differance. (shrink)

This paper investigates the emotional import of literary devices deployed in fiction. Reflecting on the often-favored approach in the analytic tradition that locates fictional characters, events, and narratives as sources of readers’ emotions, I attempt to broaden the scope of analysis by accounting for how literary devices trigger non-cognitive emotions. I argue that giving more expansive consideration to literary devices by which authors present content facilitates a better understanding of how fiction engages emotion. In doing so, I also explore the (...) somatic dimension of reading fiction. (shrink)

We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...) for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system. (shrink)

This reconsideration of Hume’s classic essay “Of Miracles” via the lens of American pragmatist ways of thinking about history and power shifts our attention from Hume’s epistemic concerns about the legitimacy of witnesses and testimony to his distaste for sacred history, his critical stance regarding the social force of revelation, and his disdain for religious authority. To view Hume’s essay both as an articulation of a critical philosophy of history and as an exercise in moral dynamism (social power or, authority, (...) is a result of epistemic transactions), is to intervene in both Hume studies and Contemporary Pragmatism. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken. (shrink)

This book presents translations of three dialogues Xenophon devoted to the life and thought of his teacher, Socrates. Each is accompanied by notes and an interpretative essay that will introduce new readers to Xenophon and foster further reflection in those familiar with his writing. "Apology of Socrates to the Jury" shows how Socrates conducted himself when he was tried on the capital charge of not believing in the city's gods and corrupting the young. Although Socrates did not secure his own (...) acquittal, he profoundly impressed some listeners who then helped to shape the public perception of philosophy as a noble, if highly idiosyncratic, way of life. In "Oeconomicus," Xenophon relates the conversation Socrates had on the day he turned from the study of natural philosophy to that of moral and political matters. "Oeconomicus" is concerned most directly with the character and purpose of Socrates' political philosophy. Xenophon provides entertaining portraits of Socrates' circle of friends in the "Symposium." In the process, he conveys the source of every individual's pride in himself, thus defining for each a conception of human excellence or virtue. The dialogue concludes with Socrates' beautiful speech on love (eros) and its proper place in the good or happy life. (shrink)