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)

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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

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)

In this book, Carlos Montemayor and Harry Haladjian consider the relationship between consciousness and attention. The cognitive mechanism of attention has often been compared to consciousness, because attention and consciousness appear to share similar qualities. But, Montemayor and Haladjian point out, attention is defined functionally, whereas consciousness is generally defined in terms of its phenomenal character without a clear functional purpose. They offer new insights and proposals about how best to understand and study the relationship between consciousness and attention (...) by examining their functional aspects. The book's ultimate conclusion is that consciousness and attention are largely dissociated. -/- Undertaking a rigorous analysis of current empirical and theoretical work on attention and consciousness, Montemayor and Haladjian propose a spectrum of dissociation—a framework that identifies the levels of dissociation between consciousness and attention—ranging from identity to full dissociation. They argue that conscious attention, the focusing of attention on the contents of awareness, is constituted by overlapping but distinct processes of consciousness and attention. Conscious attention, they claim, evolved after the basic forms of attention, increasing access to the richest kinds of cognitive contents. -/- Montemayor and Haladjian's goal is to help unify the study of consciousness and attention across the disciplines. A focused examination of conscious attention will, they believe, enable theoretical progress that will further our understanding of the human mind. (shrink)

The connection between quantum physics and the mind has been debated for almost a hundred years. There are several proposals as to how quantum effects might be relevant to understanding consciousness, including von Neumann’s Consciousness Causes Collapse interpretation (CCC), Penrose’s Orchestrated objective reduction (Orch OR), Atmanspacher quantum emergence theory, or Vitiello’s field theory. In this paper, we examine the CCC, in particular Stapp’s theory of interaction of mind and matter, and discuss how this imposes constraints to possible brain structures. We (...) then argue that those constraints may allow us to identify a possible locus of the interaction between mind and matter, if CCC is true. (shrink)

The main thesis of this paper is that two prevailing theories about cognitive penetration are too extreme, namely, the view that cognitive penetration is pervasive and the view that there is a sharp and fundamental distinction between cognition and perception, which precludes any type of cognitive penetration. These opposite views have clear merits and empirical support. To eliminate this puzzling situation, we present an alternative theoretical approach that incorporates the merits of these views into a broader and more nuanced explanatory (...) framework. A key argument we present in favor of this framework concerns the evolution of intentionality and perceptual capacities. An implication of this argument is that cases of cognitive penetration must have evolved more recently and that this is compatible with the cognitive impenetrability of early perceptual stages of processing information. A theoretical approach that explains why this should be the case is the consciousness and attention dissociation framework. The paper discusses why concepts, particularly issues concerning concept acquisition, play an important role in the interaction between perception and cognition. (shrink)

One of the world's most renowned theoretical physicists, Carlo Rovelli has entranced millions of readers with his singular perspective on the cosmos. In Helgoland, Rovelli examines the enduring enigma of quantum theory. The quantum world Rovelli describes is as beautiful as it is unnerving. Helgoland is a treeless island in the North Sea where the 21-year-old Werner Heisenberg first developed quantum theory, setting off a century of scientific revolution. Full of alarming ideas (ghost waves, distant objects that seem to be (...) magically connected, cats that appear both dead and alive), quantum physics has led to countless discoveries and technological advancements. Today our understanding of the world is based on this theory, yet it is still profoundly mysterious. As scientists and philosophers continue to fiercly debate the theory's meaning, Rovelli argues that its most unsettling contradictions can be explained by seeing the world as fundamentally made of relationships, not substances. We and everything around us exist only in our interactions with one another. This bold idea suggests new directions for understanding the structure of reality and even the nature of consciousness. Rovelli makes learning about quantum mechanics an almost psychedelic experience. Shifting our perspective once again, he takes us on a riveting journey through the universe so we can better understand our place in it. (shrink)

Ensayo introductorio para mi traducción del influyente artículo "Essence and Modality" de Kit Fine.

The definitive account of Aristotle's life and school This definitive biography shows that Aristotle's philosophy is best understood on the basis of a firm knowledge of his life and of the school he founded. First published in Italian, and now translated, updated, and expanded for English readers, this concise chronological narrative is the most authoritative account of Aristotle's life and his Lyceum available in any language. Gathering, distilling, and analyzing all the evidence and previous scholarship, Carlo Natali, one of the (...) world's leading Aristotle scholars, provides a masterful synthesis that is accessible to students yet filled with evidence and original interpretations that specialists will find informative and provocative. Cutting through the controversy and confusion that have surrounded Aristotle's biography, Natali tells the story of Aristotle's eventful life and sheds new light on his role in the foundation of the Lyceum. Natali offers the most detailed and persuasive argument yet for the view that the school, an important institution of higher learning and scientific research, was designed to foster a new intellectual way of life among Aristotle's followers, helping them fulfill an aristocratic ideal of the best way to use the leisure they enjoyed. Drawing a wealth of connections between Aristotle's life and thinking, Natali demonstrates how the two are mutually illuminating. For this edition, ancient texts have been freshly translated on the basis of the most recent critical editions; indexes have been added, including a comprehensive index of sources and an index to previous scholarship; and scholarship that has appeared since the book's original publication has been incorporated. (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)

Minding Time: A Philosophical and Theoretical Approach to the Psychology of Time offers an innovative philosophical account of the most fundamental kinds of time representation.

Discusses the nature of choice in terms of discovering God's will, tells how to face the fear of choosing, and looks at the role of compromise.

Effective vaccines for COVID‐19 are already available to humankind. In Peru, 86 million doses were administered to cover the demand for 33 million Peruvian people. Hence, vaccination has been prioritized in groups: health personnel, subjects with pre‐existing health conditions and those over 65 years of age. However, given the social problems and the public health situation in Peru, this work defends that the priority of vaccination should be focused on the population living in extreme poverty. The method used was an (...) ethical argumentation on the distribution of scarce antiSARS‐CoV2 vaccine in Peru. This argument is based on the analysis of the Peruvian population living in extreme poverty, which presents different layers of vulnerability, and that, in the face of an eventual SARS‐CoV2 infection, these would be exacerbated one after the other, through a cascade effect. This scenario would give rise to new vulnerabilities to those already existing, causing greater damage. Vaccination efforts on this key population would give them the opportunity to continue to find ways to bring food to their homes, significantly reducing the risk of contagion in their environment and mitigating the devastating effect of the local diseases to which they are already exposed. Four objections related to this argument are raised with their corresponding responses. Priority access to the vaccine would significantly reduce the humanitarian harm to people living in extreme poverty, prevailing the principles of justice and equity. (shrink)

La humanidad ya dispone de vacunas eficaces contra el COVID‐19. En Perú se administraron 86 millones de dosis para cubrir la demanda de 33 millones de peruanos. Para ello, se ha priorizado la vacunación en grupos clave: personal de salud, sujetos con condiciones de salud preexistentes y mayores de 65 años. Sin embargo, dada la problemática social y la situación de la salud pública en Perú, este trabajo defiende que la prioridad de la vacunación debe centrarse en la población que (...) vive en extrema pobreza. El método utilizado fue una argumentación ética sobre la distribución de la vacuna contra el COVID‐19 en Perú. Esta argumentación se basa en el análisis de la población peruana que vive en extrema pobreza, la cual presenta diferentes estratos de vulnerabilidad, y que, ante una eventual infección por SARS‐CoV‐2, se irían agravando uno tras otro, a través de un efecto en cascada. Este escenario daría lugar a nuevas vulnerabilidades de las ya existentes, causando mayores daños. Los esfuerzos de vacunación en esta población clave les brindaría oportunidad de seguir encontrando formas de llevar alimentos a sus hogares, reduciendo significativamente el riesgo de contagio en su entorno y mitigando el efecto devastador de las enfermedades locales a las que ya está expuesta. Se plantean cuatro objeciones relacionadas con este argumento, con sus correspondientes respuestas. El acceso prioritario a la vacuna reduciría significativamente el daño a las personas que viven en la extrema pobreza, haciendo prevalecer los principios de justicia y equidad. (shrink)

L'idee d'une multiplicite de causes, introduite dans la philosophie grecque a partir des dialogues de Platon, a trouve chez Aristote sa realisation grandiose et complexe.La discussion sur les causes a l'epoque hellenistique et imperiale confirme l'importance et l'extreme richesse de cette idee. Le titre du volume veut souligner les rapports dialectiques, parfois conflictuels et souvent polemiques, que les doctrines de la causalite de cette epoque presentent entre elles, aussi bien de maniere independante que et par rapport a la systematisation aristotelicienne. (...) Les principaux auteurs (Theophraste, Alexandre d'Aphrodise, Plotin) et les principales ecoles philosophiques (Peripatetique, Stoicienne, Epicurienne, Sceptique) de l'age hellenistique et imperial y ont ete abordes dans le but de produire un apercu le plus complet et le plus articule possible du probleme de la causalite a cette epoque. (shrink)

In this article, Carlos Pereda introduces the concept of “colonial reason” and explores how philosophical practices and modes of thought are entwined with colonial political structures of exploitation, exclusion, and oppression. Pereda argues that philosophy in Latin America risks perpetuating and reinforcing the colonial gesture, either by turning to the European centers of thought (thus pursuing debates that always take place elsewhere) or by isolating itself and idealising the “own.” According to Pereda, both approaches fail to dismantle colonial violence (...) within philosophy. In his alternative approach, Pereda outlines principles and methodological criteria for the decolonisation of reason and philosophy. He emphasises the importance of methodological prudence that discerns between innocent, paralysing, and strategic uses of identity expressions and advocates for modes of reading and argumentation that conceive philosophy as an inclusive and ongoing dialogue. In Pereda’s terminology, this entails fostering “permeable reason” that manifests itself through “nomadic thinking,” a form of thinking that is capable of questioning itself and being questioned. (shrink)

In this paper, we present one of the main starting points of naturalism in ethics: Geach’s challenge against non-cognitivism. We try to find an answer to Geach’s challenge in the notion of family resemblance applied to ethics. In doing so we recover a not much-discussed influence of Moore on Wittgenstein’s conception of family resemblance, which leads us to define Wittgenstein as non-non-cognitivist in ethics. -/- Pre print (some changes in the published edition).