Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed (...) a “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory, exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced by any given (...) class='Hi'>modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal geometrisation of this logic. (shrink)

Beall and Restall 2000; 2001; 2006 advocate a comprehensive pluralist approach to logic, which they call Logical Pluralism, according to which there is not one true logic but many equally acceptable logical systems. They maintain that Logical Pluralism is compatible with monism about metaphysical modality, according to which there is just one correct logic of metaphysical modality. Wyatt 2004 contends that Logical Pluralism is incompatible with monism about metaphysical modality. We first suggest that if Wyatt were right, Logical Pluralism would (...) be strongly implausible because it would get upside down a dependence relation that holds between metaphysics and logic of modality. We then argue that Logical Pluralism is prima facie compatible with monism about metaphysical modality. (shrink)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, (...) the present paper establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an (...) epistemic interpretation of the broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)

Graphs are among the most frequently used structures in Computer Science. Some of the properties that must be checked in many applications are connectivity, acyclicity and the Eulerian and Hamiltonian properties. In this work, we analyze how we can express these four properties with modal logics. This involves two issues: whether each of the modal languages under consideration has enough expressive power to describe these properties and how complex it is to use these logics to actually test whether (...) a given graph has some desired property. First, we show that these properties are not definable in a basic modal logic or in any bisimulation-invariant extension of it, like the modal μ-calculus. We then show that it is possible to express some of the above properties in a basic hybrid logic. Unfortunately, the Hamiltonian and Eulerian properties still cannot be efficiently checked. In a second attempt, we propose an extension of CTL* with nominals and show that the Hamiltonian property can be more efficiently checked in this logic than in the previous one. In a third attempt, we extend the basic hybrid logic with the ↓ operator and show that we can check the Hamiltonian property with optimal complexity in this logic. Finally, we tackle the Eulerian property in two different ways. First, we develop a generic method to express edge-related properties in hybrid logics and use it to express the Eulerian property. Second, we express a necessary and sufficient condition for the Eulerian property to hold using a graded modal logic. (shrink)

Charles Peirce's diagrammatic logic — the Existential Graphs — is presented as a tool for illuminating how we know necessity, in answer to Benacerraf's famous challenge that most ‘semantics for mathematics’ do not ‘fit an acceptable epistemology’. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the particular structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not merely to individual (...) things but to how those things are related in larger structures, certain aspects of which relations force certain other aspects to be a certain way. (shrink)

This paper presents the topological arrangements in four geometrical figures of modal propositions and their derivative relations by means of Peirce's gamma graphs and their rules of transformation. The idea of arraying the gamma graphs in a geometric and symmetrical order comes from Peirce himself who in a manuscript drew two cubes in which he presented the derivative relations of some gamma graphs. Therefore, Peirce's insights of a topological order of gamma graphs are extended here backwards from the cube (...) to the line and the square; and then forwards from the cube to the four-dimensional polyhedron. (shrink)

We show that there exist 2 ℵ 0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of (...) Thomason). The constructions use the result of Erd $\H{o}$ s that there are finite graphs with arbitrarily large chromatic number and girth. (shrink)

The chapter defends an evolutionary explanation of modal knowledge from knowledge of counterfactual conditionals. Knowledge of counterfactuals is evolutionarily useful, as it enables us to learn from mistakes. Given the standard semantics for counterfactuals, there are several equivalences between modal claims and claims involving counterfactuals that can be used to explain modal knowledge. Timothy Williamson has suggested an explanation of modal knowledge that draws on the equivalence of ‘Necessarily p’ with ‘If p were false, a contradiction (...) would be the case’. He postulates a cognitive process that draws on this equivalence and that is supposed to underlie our modal judgements. The existence of this cognitive process would, however, have consequences that conflict with results from empirical psychology. The chapter argues that the equivalence of ‘Necessarily p’ with ‘For all q, if q were true then p would be true’ should instead be used to explain knowledge of necessity. This explanation requires giving an account of how we know truths of the form ‘For all q, if q were true then p would be true’. In order to provide such an account, the chapter draws on a different suggestion by Williamson about knowledge of generalizations. According to this suggestion, we come to know truths of the form ‘All Fs are G’ by imagining a generic F and judging that it is G. Applied to our case, the suggestion would be that we come to know that p is counterfactually implied by all propositions (and hence that p is necessary) by entertaining a generic proposition and judging that it counterfactually implies p. It would even suffice to entertain a generic possible proposition and judge that it counterfactually implies p, for it can be shown that the claim ‘For all possible q, if q were true then p would be true’ is equivalent to the original claim ‘For all q, if q were true then p would be true’ and hence is equivalent to ‘Necessarily p’. It might seem that, from an evolutionary perspective, probabilistic reasoning is just as useful as reasoning involving counterfactuals. The chapter argues, however, that this would not undermine the envisaged explanation of modal knowledge. The chapter concludes by suggesting avenues of empirical research that might shed light on the cognitive processes that actually underlie our evaluations of modal claims and on the relation between these processes and those involved in counterfactual reasoning. The results of such empirical research would be highly relevant epistemologically, since they will ultimately determine which (if any) equivalence between modal claims and claims involving counterfactuals should be used to explain our modal knowledge. (shrink)

We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (MLSR) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a (...) complete Hillbert-style axiomatization for the logic of stepwise removal in a hybrid language enriched with nominals and public announcement operators. Next, we show that model-checking for MLSR is PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we consider an issue of fine-structure: the expressive power gained by adding the stepwise removal modality to fragments of first-order logic. (shrink)

Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. In this work, we develop a general framework—the supervised learning game—to investigate the interaction between Teacher and Learner. In particular, our proposal highlights several interesting features of the agents: on the one hand, Learner may make mistakes in the learning process, and she may also ignore the potential relation between different hypotheses; on the other (...) hand, Teacher is able to correct Learner’s mistakes, eliminate potential mistakes and point out the facts ignored by Learner. To reason about strategies in this game, we develop a modal logic of supervised learning and study its properties. Broadly, this work takes a small step towards studying the interaction between graph games, logics and formal learning theory. (shrink)

Peirce introduced Existential Graphs in late 1896, and they were systematically investigated in his 1903 Lowell Lectures. Alpha graphs for classical propositional logic constitute the first part of EGs. The second and the third parts are the beta graphs for first-order logic and the gamma graphs for modal and higher-order logics, among others. As a logical syntax, EGs are two-dimensional graphs, or diagrams, in contrast to the linear algebraic notations. Peirce's theory of EGs is not only a theory of (...) logical syntax but also a proof theory for many logics. A set of transformation rules of graphs defines a proof system for a graphical logic. In this... (shrink)

We consider modal logics whose intermediate fragments lie between the logic of infinite problems [20] and the Medvedev logic of finite problems [15]. There is continuum of such logics [19]. We prove that none of them is finitely axiomatizable. The proof is based on methods from [12] and makes use of some graph-theoretic constructions (operations on coverings, and colourings).

A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a (...) modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra's generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott's graph model (for the untyped lambda calculus) which witnesses the failure of the stability of non-identity. (shrink)

A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of (...) this interpretation by axiomatizing some natural subclasses of reactive frames. The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques. (shrink)

Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A well-known example from the literature on intuitionistic logic is the class of Medvedev frames $\langle W,R\rangle$ where $W$ is the set of nonempty subsets of some nonempty finite set $S$, and $xRy$ iff $x\supseteq y$, or more liberally, where (...) $\langle W,R\rangle$ is isomorphic as a directed graph to $\langle \wp(S)\setminus\{\emptyset\},\supseteq\rangle$. Prucnal [32] proved that the modal logic of Medvedev frames is not finitely axiomatizable. Here we continue the study of Medvedev frames with extended modal languages. Our results concern definability. We show that the class of Medvedev frames is definable by a formula in the language of tense logic, i.e., with a converse modality for quantifying over supersets in Medvedev frames, extended with any one of the following standard devices: nominals (for naming nodes), a difference modality (for quantifying over those $y$ such that $x\not= y$), or a complement modality (for quantifying over those $y$ such that $x\not\supseteq y$). It follows that either the logic of Medvedev frames in one of these tense languages is finitely axiomatizable---which would answer the open question of whether Medvedev's [31] "logic of finite problems'' is decidable---or else the minimal logics in these languages extended with our defining formulas are the beginnings of infinite sequences of frame-incomplete logics. (shrink)

Charles Peirce incorporates modality into his Existential Graphs by introducing the broken cut for possible falsity. Although it can be adapted to various modern modal logics, Zeman demonstrates that making no other changes results in a version that he calls Gamma-MR, an implementation of Jan Łukasiewicz's four-valued Ł-modal system. It disallows the assertion of necessity, reflecting a denial of determinism, and has theorems involving possibility that seem counterintuitive at first glance. However, the latter is a misconception that arises (...) from overlooking the distinction between the intermediate truth values that are assigned to possibly true propositions as either X-contingent or Y-contingent. Any two propositions having the same ITV are possible together, while any two propositions having different ITVs, including those that are each other's negation, are possible individually yet not possible together. Porte shows that Ł-modal can be translated into classical logic by defining a constant for each ITV such that its implication of another proposition asserts the latter's possibility, while its conjunction with another proposition asserts the latter's necessity. These are expressed in the Alpha part of EG without broken cuts, simplifying derivations and shedding further light on Łukasiewicz's system, as long as graphs including either of the constants are properly interpreted. Ł-modal and Gamma-MR thus capture the two-sided nature of possibility as the limit between truth and falsity in Peirce's triadic conception. (shrink)

In this paper we develop the theoretical foundations to exploit symmetries in modal logics. We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas using the framework provided by coinductive modal models introduced in [5]. Hence, the results apply to a wide class of modal logics including, for example, hybrid logics. We present two graph constructions that enable the reduction of symmetry detection in modal formulas to the (...) class='Hi'>graph automorphism detection problem, and we evaluate the graph constructions on modal benchmarks. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- (...) This dissertation focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

L’epistemologia (detta anche filosofia della conoscenza o gnoseologia) è la disciplina filosofica che studia come gli esseri umani si rapportano da un punto di vista cognitivo alla realtà che li circonda. Le questioni fondamentali che la interessano sono principalmente di natura normativa. Riguardano il modo in cui dovremmo regolare le nostre credenze alla luce dell’informazione in nostro possesso, e la natura della conoscenza umana ed i suoi limiti. Questo capitolo è organizzato in modo corrispondente. La prima sezione tratta della nozione (...) di giustificazione epistemica, la seconda quella di conoscenza, e la terza introduce il problema filosofico dello scetticismo. (shrink)

In this monograph we contrast two prominent models of education, Competence-Based Education (CBE), more recent and currently dominant in most school systems of the world, and Bildung-Oriented Education (BOE), once the basis of school systems of Northern Europe. CBE interprets learning as the acquisition of clearly definable and allegedly measurable competences, and is supported by supranational organisations, such as the OECD, which approach education from the perspective of the human capital theory. BOE instead characterises learning holistically as aimed at the (...) progressive articulation of a meaningful ‘big picture’ in the student’s mind. Emerged in Northern Europe under the influence of the ideals of the Enlightenment and Neo-Humanism of individual and collective autonomy and responsibility, BOE was subsequently enriched with a hermeneutical approach to teaching and socio-political objectives of emancipation and solidarity originating within Critical Theory. We argue that, in spite of its celebrated ‘scientificity’, CBE is internally incoherent and unreliable, contributes to structural forms of oppression and injustice, fosters social pathologies, and fails to provide students with the kind of intellectual autonomy they need as both human beings and citizens of our complex post-industrial societies. We also defend BOE from objections made by critical theorists, poststructuralists and postcolonial thinkers, and argue that it is a coherent and flexible model of education that endows students with autonomy and responsibility, and can help heal social pathologies. (shrink)

We focus on issues of learning assessment from the point of view of an investigation of philosophical elements in teaching. We contend that assessment of concept possession at school based on ordinary multiple-choice tests might be ineffective because it overlooks aspects of human rationality illuminated by Robert Brandom’s inferentialism––the view that conceptual content largely coincides with the inferential role of linguistic expressions used in public discourse. More particularly, we argue that multiple-choice tests at schools might fail to accurately assess the (...) possession of a concept or the lack of it, for they only check the written outputs of the pupils who take them, without detecting the inferences actually endorsed or used by them. We suggest that school tests would acquire reliability if they enabled pupils to make the reasons of their answers or the inferences they use explicit, so as to contribute to what Brandom calls the game of giving and asking for reasons. We explore the possibility to put this suggestion into practice by deploying two-tier multiple-choice tests. (shrink)

Phenomenal Conservatism (the view that an appearance that p gives one prima facie justification for believing that p) is a promising, and popular, internalist theory of epistemic justification. Despite its popularity, it faces numerous objections and challenges. For instance, epistemologists have argued that Phenomenal Conservatism is incompatible with Bayesianism, is afflicted by bootstrapping and cognitive penetration problems, does not guarantee that epistemic justification is a stable property, does not provide an account of defeat, and is not a complete theory of (...) epistemic justification. This book shows that Phenomenal Conservatism is actually immune to some of these problems, though not all of them. Accordingly, it explores the prospects of integrating Phenomenal Conservatism with Explanationism (the view that epistemic justification is a matter of explanatory relations between one’s evidence and propositions supported by that evidence). The resulting theory, Phenomenal Explanationism, has advantages over Phenomenal Conservatism and Explanationism taken on their own. Phenomenal Explanationism is a highly unified, comprehensive internalist theory of epistemic justification that delivers on the promises of Phenomenal Conservatism while avoiding its pitfalls. (shrink)

In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...) extend each of the three representations to lattices with a multiplicative unary modality; the representing structures, like so-called graph-based frames, add a second relation of accessibility interacting with compatibility. The three representations generalize possibility semantics for classical modal logics to non-classical modal logics, motivated by a recent application of modal orthologic to natural language semantics. (shrink)

The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs.

Recent advances in neuroscience indicate that analysis of bio-signals such as rest state electroencephalogram and eye-tracking data can provide more reliable evaluation of children autism spectrum disorder than traditional methods of behavior measurement relying on scales do. However, the effectiveness of the new approaches still lags behind the increasing requirement in clinical or educational practices as the “bio-marker” information carried by the bio-signal of a single-modality is likely insufficient or distorted. This study proposes an approach to joint analysis of EEG (...) and eye-tracking for children ASD evaluation. The approach focuses on deep fusion of the features in two modalities as no explicit correlations between the original bio-signals are available, which also limits the performance of existing methods along this direction. First, the synchronization measures, information entropy, and time-frequency features of the multi-channel EEG are derived. Then a random forest applies to the eye-tracking recordings of the same subjects to single out the most significant features. A graph convolutional network model then naturally fuses the two group of features to differentiate the children with ASD from the typically developed subjects. Experiments have been carried out on the two types of the bio-signals collected from 42 children. The results indicate that the proposed approach can achieve an accuracy of 95% in ASD detection, and strong correlations exist between the two bio-signals collected even asynchronously, in particular the EEG synchronization against the face related/joint attentions in terms of covariance. (shrink)

Åsa Burman has recently introduced the important notion of telic power and differentiated it from deontic power in an attempt to build a bridge between ideal and non-ideal social ontology. We find Burman’s project promising but we argue that more is to be done to make it entirely successful. First, there is a palpable tension between Burman’s claim that telic power can be ontologically independent of deontic power and her examples, which suggest that these forms of power share the same (...) basis. Second, it is not completely clear how telic power helps non-ideal social ontologists explain oppression, since Burman thinks that both forms of power are transparent to social agents. We offer solutions to both problems. First, we question the thesis that telic power can exist without deontic power. Burman contends that this is possible because some social roles involving telic power can exist independently of institutions, which are––in her opinion––the source of deontic power. Against Burman, we suggest that all social roles involve deontic power, whether or not they are institutional. Second, we argue that while the exercise of deontic power requires a mutual recognition of the social roles of the interacting agents and, therefore, an acceptance of the associated norms, the exercise of telic power does not require acceptance of the relevant norms. This is why invoking telic power is useful in explaining how oppression and injustice can arise. Lastly, we suggest that the relation between teleological normativity and telic power has not been fully clarified by Burman and requires a deeper analysis. (shrink)

Perceptual experience is one of our fundamental sources of epistemic justification—roughly, justification for believing that a proposition is true. The ability of perceptual experience to justify beliefs can nevertheless be questioned. This article focuses on an important challenge that arises from countenancing that perceptual experience is cognitively penetrable. -/- The thesis of cognitive penetrability of perception states that the content of perceptual experience can be influenced by prior or concurrent psychological factors, such as beliefs, fears and desires. Advocates of this (...) thesis could for instance claim that your desire of having a tall daughter might influence your perception, so that she appears to you to be taller than she is. Although cognitive penetrability of perception is a controversial empirical hypothesis, it does not appear implausible. The possibility of its veracity has been adduced to challenge positions that maintain that perceptual experience has inherent justifying power. -/- This article presents some of the most influential positions in contemporary literature about whether cognitive penetration would undermine perceptual justification and why it would or would not do so. -/- Some sections of this article focus on phenomenal conservatism, a popular conception of epistemic justification that more than any other has been targeted with objections that adduce the cognitive penetrability of experience. (shrink)

We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a (...) class of non-wellfounded proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations. (shrink)

In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fitting's many-valued modal languages. These languages were introduced by M. Fitting in the early '90s and are built on Heyting algebras which serve as the space of truth values. The possible-worlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of many-valued accessibility relation. Weak (...) axioms of the form we treat here have been examined from the completeness perspective and further explored for applications in non-monotonic reasoning. Here, we introduce more weak many-valued modal axioms and prove a frame correspondence result for all of them. The classes of corresponding labelled frames possess algebraic properties which are strongly reminiscent of many classical ones, such as the Church-Rosser property, reflexivity, transitivity, partial functionality, etc. (shrink)

This paper connects the following three apparently unrelated topics: an epistemic framework fighting logical omniscience, a class of generalized graphs without the arities of relations, and a family of non-normal modal logics rejecting the aggregative axiom. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained in this paper, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs and also the epistemic logic of local reasoning (...) with veracity and positive introspection. The logics studied are shown to be decidable based on a filtration construction. (shrink)

The role of academic satisfaction on persistence and successful academic behavior has been the focus of research for decades. Nevertheless, driven by positive educational psychology, subjective well-being has been highlighted as another central feature in the academic path of students. Studies aimed at identifying the variables that contribute to explain different aspects of academic performance have been widely investigated, although studies aimed at identifying the determinants of subjective well-being are still limited. The present paper examined the contribution of AS judgments (...) on subjective well-being. To this end, it was hypothesized that SWB levels depend on the balance between positive/negative emotions and life satisfaction judgments. Furthermore, it was stipulated that AS has an indirect contribution on SWB, through life satisfaction, whereas the balance of emotions influences both AS judgments and life satisfaction. Using an analysis strategy based on structural equation modeling, the results indicated that the model fitted satisfactorily, explaining 32% of the variance of SWB. Particularly, it was observed that AS judgments contributed to life satisfaction judgments. Although no direct contribution of AS on SWB was reported, a total contribution partially mediated by life satisfaction judgments was revealed. These findings support the importance of academic satisfaction judgments, not only because of their importance in academic terms, but also because of their impact on university students’ subjective well-being and health. (shrink)

We present novel proof systems for various FDE-based modal logics. Among the systems considered are a number of Belnapian modal logics introduced in Odintsov & Wansing and Odintsov & Wansing, as well as the modal logic KN4 with strong implication introduced in Goble. In particular, we provide a Hilbert-style axiom system for the logic $BK^{\square - } $ and characterize the logic BK as an axiomatic extension of the system $BK^{FS} $. For KN4 we provide both an (...) FDE-style axiom system and a decidable sequent calculus for which a contraction elimination and a cut elimination result are shown. (shrink)

Philosophers have claimed that education aims at fostering disparate epistemic goals. In this paper we focus on an important segment of this debate involving conversation between Alvin Goldman and Harvey Siegel. Goldman claims that education is essentially aimed at producing true beliefs. Siegel contends that education is essentially aimed at fostering both true beliefs and, independently, critical thinking and rational belief. Although we find Siegel’s position intuitively more plausible than Goldman’s, we also find Siegel’s defence of it wanting. We suggest (...) novel argumentative strategies that draw on Siegel’s own arguments but look to us more promising. (shrink)

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

This is the introduction to Moretti, Luca and Nikolaj Pedersen (eds), Non-Evidentialist Epistemology. Brill. Contributors: N. Ashton, A. Coliva, J. Kim, K. McCain, A. Meylan, L. Moretti, S. Moruzzi, J. Ohlorst, N. Pedersen, T. Piazza, L. Zanetti.

This paper deals with modality in Peirce's existential graphs, as expressed in his gamma and tinctured systems. We aim at showing that there were two philosophically motivated decisions of Peirce's that, in the end, hindered him from producing a modern, conclusive system of modal logic. Finally, we propose emendations and modifications to Peirce's modal graphical tinctured systems and to their underlying ideas that will produce modern modal systems.