Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.

Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...) Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. (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)

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...) An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (shrink)

Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula (...) nor its converse hold. (shrink)

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The “truth-values as (...) labels” approach allows us to give generalized systems for multiple-valued logics within the same formalism: since we can take multiple-valued logics as meaning not only finitely or infinitely many-valued logics but also power-set logics, i.e. logics for which the denotation of a formula can be seen as a set of worlds, our recipe allows us to capture also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards the fibring of these logics with many-valued ones. (shrink)

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way . Heterogeneous fibring, allowing the original logics to have different presentations , has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus (...) and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated. (shrink)

Cut elimination is shown, in a constructive way, to hold in sequent calculi labelled with truth values for a wide class of normal modal logics, supporting global and local reasoning and allowing a general frame semantics. The complexity of cut elimination is studied in terms of the increase of logical depth of the derivations. A hyperexponential worst case bound is established. The subformula property and a similar property for the label terms are shown to be satisfied by that class of (...) modal sequent calculi. Modal logics presented by these calculi are proven to be globally and locally consistent. (shrink)

Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural two-sorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result (...) is established between the category of sober algebras and the category of general Kripke structures. A simple enrichment of the proposed sequent calculi is proved to be complete over standard Kripke structures. The calculi are shown to be analytic in a useful sense. (shrink)

Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...) the meet-combination is proved to be decidable whenever the validity problem for the components are decidable. Several examples are discussed, namely, involving modal and intuitionistic logics, as well as the meet-combination of modal logic and intuitionistic logic. (shrink)

The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous (...) enrichment. (shrink)

A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear logic, a Kolmogorov-Gentzen-Gödel style translation, and a new translation between (...) the global consequence systems induced by full Lambek calculus and linear logic, mixing features of a Kiriyama-Ono style translation with features of a Kolmogorov-Gentzen-Gödel style translation. These translations establish a strong relationship between the logics involved and are used to obtain new results about whether Craig interpolation and Maehara interpolation hold in that logics . (shrink)

The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...) a schema formula. Based on these concepts we prove general robustness results that relate the complexity of introducing a logical constructor with the complexity of the component schema formulas as well as the complexity of a schema formula across different schema calculi. (shrink)

Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical approach of fusion (...) is defined in the context of these logic systems. Preservation of soundness and completeness by fusion is studied. Soundness is preserved without further requirements, completeness is preserved under mild assumptions. (shrink)

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. (...) We introduce the time-stamped claim logic including a sound and complete sequent calculus. In order to show how time-stamped claim logic can be used in practice, we consider a concrete cyber-attribution case study. (shrink)

We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures.

Health care is ubiquitous in the industrialized world. Yet, every medical development, technique, and procedure impacts the environment. Green bioethics synthesizes environmental ethics and biomedical ethics, thus creating an interdisciplinary approach to sustainable health care. Notably, green bioethics addresses not the structure of environmental sustainability in health-care institutions but the sustainability of individual health-care offerings. It parallels traditional biomedical ethics by providing four principles for ethical guidance: distributive justice, resource conservation, simplicity, and ethical economics. Through these four principles, green bioethics (...) presents a coherent framework for evaluating the sustainability of medical developments, techniques, and procedures. The future of our world may very well depend on how effectively we halt ecological destruction and conserve our resources in all areas of life. The principles of green bioethics, outlined in this book, will advance sustainability in health care. (shrink)

Griefbots are chatbots designed to assist individuals in coping with the loss of a loved one by offering a digital replica of the departed. Navigating grief is a deeply transformative and vulnerable journey intricately tied to one's well-being. Do griefbots aid in the grieving process, or do they complicate it? To address these questions, this article blends insights from philosophy and neuroscience to explore the nature of grief as a means to clarify the ethical dimensions surrounding the use of griefbots.

L.A. Paul calls “deep” the kind of essentialism according to which the essential properties of objects are determined independently of the context. Deep essentialism opposes “shallow essentialism”, of which David Lewis is said to be a prominent advocate. Paul argues that standard forms of deep essentialism face a range of issues (mainly based on an interpretation of Quinean skepticism) that shallow essentialism does not. However, Paul claims, shallow essentialism eliminates the very heart of what motivates essentialism, so it is better (...) to be deep than shallow. Accordingly, she proposes a very sharp novel account of essentialism, which, while attempting to preserve some of the advantages of shallow essentialism over the classical forms of deep essentialism, can be deemed to be deep. In this paper, I compare Paul’s proposal for a kind of deep essentialism with Lewis’s account, as it is presented by Paul. My aim is to show that the differences between the two approaches are not as significant as Paul takes them to be, and that Paul’s account can be taken to be deeper than Lewis’s only at the cost of sacrificing the very idea at the bottom of deep essentialism. This might be taken to suggest that, if Paul is correct in asserting that shallow essentialism is better equipped to address some skeptical challenges, but it is generally preferable to be deep than shallow, then Lewis’s account should be re-evaluated, since, as shallow as it can be, it might be deeper than it looks. (shrink)

InA Theory of Justice, Rawls claims that “to each according to his threat advantage is not a conception of justice.” Although it may indeed seem intuitively plausible that a principle based on “threat advantage” cannot count as a principle of justice, it is an altogether different matter to explain why this is so. The question is especially pressing if one bears in mind that such a principle of bargaining in fact underlies many institutionally regulated interactions. Moreover, to the extent that (...) morality is thought of as a mechanism for guaranteeing mutual advantage in the resolution of conflicts, it may indeed seem necessary that it reflect the bargaining power of the parties (in order to make sure that it is indeed advantageous for all of them). In fact, there is a prominent tradition of social-contract theories (from Hobbes to Gauthier) that work under this assumption and claim to provide an answer to what justice requires as much as Rawls's theory does. So seen, the burden of proof seems to fall rather on the shoulders of those committed to claim both that morality is a mechanism that works to the advantage of all and that it nevertheless requires neutralizing all differences in bargaining power. (shrink)

InA Theory of Justice, Rawls claims that “to each according to his threat advantage is not a conception of justice.” Although it may indeed seem intuitively plausible that a principle based on “threat advantage” cannot count as a principle of justice, it is an altogether different matter to explain why this is so. The question is especially pressing if one bears in mind that such a principle of bargaining in fact underlies many institutionally regulated interactions. Moreover, to the extent that (...) morality is thought of as a mechanism for guaranteeing mutual advantage in the resolution of conflicts, it may indeed seem necessary that it reflect the bargaining power of the parties (in order to make sure that it is indeed advantageous for all of them). In fact, there is a prominent tradition of social-contract theories (from Hobbes to Gauthier) that work under this assumption and claim to provide an answer to what justice requires as much as Rawls's theory does. So seen, the burden of proof seems to fall rather on the shoulders of those committed to claim both that morality is a mechanism that works to the advantage of all and that it nevertheless requires neutralizing all differences in bargaining power. (shrink)

Les études réunies et publiés dans ce volume sont d'abord concentrées sur les problèmes relatifs à la nature de l'âme en général, notamment par le biais d'une confrontation avec des penseurs antérieurs a Aristote ou qui leur sont contemporains - spécialement Platon et Xenocrate.

The aim of this article is to contribute detailed ethnographic material to broaden the scope of what we mean by reproductive technology. Technology can be defined not only by a series of laboratory techniques (such as artificial insemination and embryo transfer) that are drafted into the daily management of the animal body, but also by a range of on-farm management strategies and working routines, as well as the cultural dispositions, social networks and tacit knowledge of the actors involved. RT is (...) communicated to lay operators and disseminated amongst semi-professional figures such as breed experts, herd inspectors and technical consultants. The practical contexts in which reproductive knowledge is popularized and applied provide ample scope for local negotiations, resistance and conflict. Professional knowledge about breed-improvement is personalised and appropriated by operators and plays a role in power relations and the exercise of personal charisma as well as being specific to context, in particular the nuances of pre-existing relationships of trust, friendship, kinship or hierarchy. No wonder then that many ambivalences and compromises coexist in the practice of applying ‘reproductive knowledge’ to breed selection. (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)

This book offers a collection of reflective essays on current testimonial production by researchers and practitioners working in multifaceted fields such as art and film performance, public memorialization, scriptotherapy, and fictional and non-fictional testimony. 0The inter-disciplinary approach to the question of testimony offers a current account of testimony's diversity in the twenty-first century as well as its relevance within the fields of art, storytelling, trauma, and activism. The range of topics engage with questions of genre and modes of representation, ethical (...) and political concerns of testimony, and the flaws and limitations of testimonial production giving testament to some of the ethical concerns of our present age. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...) m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better (...) understanding of what are the common properties of any two constructors, say disjunction and conjunction. (shrink)

The paper addresses the methodology used by the teacher-KEYWORDS: facilitator to plan P4C sessions. The classic method consists of identifying the guidelines of the dialogue from a provisional mapping of the text, but this can be supplemented or replaced by other tools‡. GrupIREF and the Filosofía Lúdica movement§ use an approach that focuses on thinking skills. The P4C session is planned from the choice of the thinking skills to be trained - or possibly the attitudes and ethical values that appear (...) in the stimulus used. This article proposes an alternative to the classical planning approach, examining the basis of the model considered and offering a practical example. ITA_Focus dell’articolo è la modalità di pianificazione delle sessioni di Philosophy for Children, P4C, da parte del docente-facilitatore. Il metodo classico consiste nell’individuazione di linee-guida del dialogo a partire da una mappatura orientativa del testo-pretesto, ma ciò può essere integrato, o sostituito da altre modalità*. Il GrupIREF e il movimento della Filosofía Lúdica† utilizzano un approccio che privilegia le abilità di pensiero. La sessione P4C viene pianificata a partire dalla scelta dell’abilità di pensiero da allenare – o eventualmente dell’atteggiamento etico e dei valori legati al pre-testo utilizzato. Il presente lavoro suggerisce un’alternativa alla progettazione classica, attraverso una disamina delle basi del modello considerato, e ne offre un esempio pratico. (shrink)

Our lives are commonly involved with fictionality, an activity that adults share with children. After providing a brief reconstruction of the most important cognitive theories on pretence, we will argue that pretence has to do with metarepresentations, albeit in a rather weakened sense. In our view, pretending entails being aware that a certain representation does not fit in the very same representational model as another representation. This is a minimal metarepresentationalism, for normally metarepresentationalism on pretense claims that pretending is or (...) entails representing a representation qua representation, i.e. as conceptualised as a representation, in its very content. In the final section we will try to draw some consequences of our view as to the debate in cognitive science on mindreading. Given this minimal metarepresentationalism, the two main positions on mindreading, the ‘theory theory’ and the ‘simulation theory’, turn out to be closer than one would have originally supposed. (shrink)

In Norms in the Wild, distinguished philosopher Cristina Bicchieri argues that when it comes to human behavior, social scientists place too much stress on rational deliberation. In fact, she says, many choices occur without much deliberation at all. Two people passing in a corridor automatically negotiate their shared space; cars at an intersection obey traffic signals; we choose clothing based on our instincts for what is considered appropriate. Bicchieri's theory of social norms accounts for these automatic components of coordination, (...) where individuals react automatically to cues that focus their attention on what the norm is in that situation. Social norms thus act as rules for making choices in a social world where people expect others -- often unconsciously -- to follow the same rule. Some norms enable seamless social co-operation, while others are less beneficial to human flourishing.Bicchieri is famous for her interdisciplinary work on game theory and most recently her work on social norms, and Norms in the Wild represents her latest challenge to many of the fundamental assumptions of the social sciences. Bicchieri's work has broad implications not only for understanding human behavior, but for changing it for better outcomes. People have a strongly conditioned preference for following social norms, but that also means that manipulating their expectations can cause major behavioral changes. Bicchieri has been working recently with UNICEF and other NGO's to explore the applicability of her views to issues of human rights around the world. Is it possible to change social expectations around forced marriage, genital mutilations, and public health practices like vaccinations and sanitation? If so, how? What tools might we use? This short book explores how social norms work, and how changing them - changing preferences, beliefs, and especially social expectations - can potentially improve lives all around the world. It will appeal to an unusually broad range of readers including philosophers, psychologists and others in behavioral sciences, and anyone involved in public policy or at NGOs. (shrink)

In The Grammar of Society, first published in 2006, Cristina Bicchieri examines social norms, such as fairness, cooperation, and reciprocity, in an effort to understand their nature and dynamics, the expectations that they generate, and how they evolve and change. Drawing on several intellectual traditions and methods, including those of social psychology, experimental economics and evolutionary game theory, Bicchieri provides an integrated account of how social norms emerge, why and when we follow them, and the situations where we are (...) most likely to focus on relevant norms. Examining the existence and survival of inefficient norms, she demonstrates how norms evolve in ways that depend upon the psychological dispositions of the individual and how such dispositions may impair social efficiency. By contrast, she also shows how certain psychological propensities may naturally lead individuals to evolve fairness norms that closely resemble those we follow in most modern societies. (shrink)