87,187 research outputs found
Constructive Provability Logic
We present constructive provability logic, an intuitionstic modal logic that
validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting
logical reflection over provability. Two distinct variants of this logic, CPL
and CPL*, are presented in natural deduction and sequent calculus forms which
are then shown to be equivalent. In addition, we discuss the use of
constructive provability logic to justify stratified negation in logic
programming within an intuitionstic and structural proof theory.Comment: Extended version of IMLA 2011 submission of the same titl
To Teach Modal Logic: An Opinionated Survey
I aim to promote an alternative agenda for teaching modal logic chiefly
inspired by the relationships between modal logic and philosophy. The guiding
idea for this proposal is a reappraisal of the interest of modal logic in
philosophy, which do not stem mainly from mathematical issues, but which is
motivated by central problems of philosophy and language. I will point out some
themes to start elaborating a guide for a more comprehensive approach to teach
modal logic, and consider the contributions of dual-process theories in
cognitive science, in order to explore a pedagogical framework for the proposed
point of view.Comment: Proceedings of the Fourth International Conference on Tools for
Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M.
Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat,
Fran\c{c}ois Schwarzentrube
Moderate Modal Skepticism
This paper examines "moderate modal skepticism", a form of skepticism about
metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal
arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism
assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems
for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a different epistemology of possibility, which does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw
Grafting Hypersequents onto Nested Sequents
We introduce a new Gentzen-style framework of grafted hypersequents that
combines the formalism of nested sequents with that of hypersequents. To
illustrate the potential of the framework, we present novel calculi for the
modal logics and , as well as for extensions of the
modal logics and with the axiom for shift
reflexivity. The latter of these extensions is also known as
in the context of deontic logic. All our calculi enjoy syntactic cut
elimination and can be used in backwards proof search procedures of optimal
complexity. The tableaufication of the calculi for and
yields simplified prefixed tableau calculi for these logic
reminiscent of the simplified tableau system for , which might be
of independent interest
Truthmakers and modality
This paper attempts to locate, within an actualist ontology, truthmakers for modal truths: truths of the form or . In section 1 I motivate the demand for substantial truthmakers for modal truths. In section 2 I criticise Armstrong’s account of truthmakers for modal truths. In section 3 I examine essentialism and defend an account of what makes essentialist attributions true, but I argue that this does not solve the problem of modal truth in general. In section 4 I discuss, and dismiss, a theistic account of the source of modal truth proposed by Alexander Pruss. In section 5 I offer a means of (dis)solving the problem
Probability in modal interpretations of quantum mechanics
Modal interpretations have the ambition to construe quantum mechanics as an
objective, man-independent description of physical reality. Their second
leading idea is probabilism: quantum mechanics does not completely fix physical
reality but yields probabilities. In working out these ideas an important motif
is to stay close to the standard formalism of quantum mechanics and to refrain
from introducing new structure by hand. In this paper we explain how this
programme can be made concrete. In particular, we show that the Born
probability rule, and sets of definite-valued observables to which the Born
probabilities pertain, can be uniquely defined from the quantum state and
Hilbert space structure. We discuss the status of probability in modal
interpretations, and to this end we make a comparison with many-worlds
alternatives. An overall point that we stress is that the modal ideas define a
general framework and research programme rather than one definite and finished
interpretation
A Formal Apology for Metaphysics
There is an old meta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form since the rise of logical positivism in the early twentieth century but has seen a bit of a renaissance recently. In this paper, I provide an apology for metaphysics in the face of this kind of concern. The core of the argument is this: pure mathematics detaches from science in much the same manner as metaphysics and yet it is valuable nonetheless. The source of value enjoyed by pure mathematics extends to metaphysics as well. Accordingly, if one denies that metaphysics has value, then one is forced to deny that pure mathematics has value. The argument places an added burden on the sceptic of metaphysics. If one truly believes that metaphysics is worthless (as some philosophers do), then one must give up on pure mathematics as well
Organising the knowledge space for software components
Software development has become a distributed, collaborative process based on the assembly of off-the-shelf and purpose-built components. The selection of software components from component repositories and the development of components for these repositories requires an accessible information infrastructure that allows the description and comparison of these components. General knowledge relating to software development is equally important in this context as knowledge concerning the application domain of the software. Both form two pillars on which the structural and behavioural properties of software components can be addressed. Form, effect, and intention are the essential aspects of process-based knowledge representation with behaviour as a primary property. We investigate how this information space for software components can be organised in order to facilitate the required taxonomy, thesaurus, conceptual model, and logical framework functions. Focal point is an axiomatised ontology that, in addition to the usual static view on knowledge, also intrinsically addresses the dynamics, i.e. the behaviour of software. Modal logics are central here – providing a bridge between classical (static) knowledge representation approaches and behaviour and process description and classification. We relate our discussion to the Web context, looking at Web services as components and the Semantic Web as the knowledge representation framewor
Epistemological vs. Ontological Relationalism in Quantum Mechanics: Relativism or Realism?
In this paper we investigate the history of relationalism and its present use
in some interpretations of quantum mechanics. In the first part of this article
we will provide a conceptual analysis of the relation between substantivalism,
relationalism and relativism in the history of both physics and philosophy. In
the second part, we will address some relational interpretations of quantum
mechanics, namely, Bohr's relational approach, the modal interpretation by
Kochen, the perspectival modal version by Bene and Dieks and the relational
interpretation by Rovelli. We will argue that all these interpretations ground
their understanding of relations in epistemological terms. By taking into
account the analysis on the first part of our work, we intend to highlight the
fact that there is a different possibility for understanding quantum mechanics
in relational terms which has not been yet considered within the foundational
literature. This possibility is to consider relations in (non-relativist)
ontological terms. We will argue that such an understanding might be capable of
providing a novel approach to the problem of representing what quantum
mechanics is really talking about.Comment: Welcome
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