|
|
- Taking Up Thagard’s Challenge: A Formal Model of Conceptual Revision
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Thagard (1992) presented a framework for conceptual change in science based on conceptual systems. Thagard challenged belief revision theorists, claiming that traditional belief-revision systems are able to model only the two most conservative types of changes in his framework, but not the more radical ones. The main aim of this work is to take up Thagard’s challenge, presenting a belief-revision-like system able to mirror radical types of conceptual change. We will do that with a conceptual revision system, i.e. a belief-revision-like system that takes conceptual structures as units of revisions. We will show how our conceptual revision and contraction operations satisfy analogous of the AGM postulates at the conceptual level and are able to mimic Thagard’s radical types of conceptual change.
PubDate: 2022-08-01
- Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry (SIG) based on certain algebraic objects (i.e., rings), which regiments a mode of reasoning heuristically used by geometricists and physicists (e.g., circle is composed of infinitely many straight lines). I argue that SIG has the following utilities. (1) It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. (2) It generalizes a standard implementation of spacetime algebraicism (according to which physical fields exist fundamentally without an underlying manifold) called Einstein algebras. (3) It solves the long-standing problem of interpreting smooth infinitesimal analysis (SIA) realistically, an alternative foundation of spacetime theories to real analysis (Lawvere Cahiers de Topologie et Géométrie Différentielle Catégoriques, 21(4), 277–392, 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations (Hellman Journal of Philosophical Logic, 35, 621–651, 2006). Against this, I argue that SIG is (part of) such a reformulation. But SIG has an unorthodox mereology, in which the principle of supplementation fails.
PubDate: 2022-08-01
- Paraconsistent Metatheory: New Proofs with Old Tools
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic(s) can be obtained' We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems.
PubDate: 2022-08-01
- Designing Paradoxes: A Revision-theoretic Approach
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: According to the revision theory of truth, the binary sequences generated by the paradoxical sentences in revision sequence are always unstable. In this paper, we work backwards, trying to reconstruct the paradoxical sentences from some of their binary sequences. We give a general procedure of constructing paradoxes with specific binary sequences through some typical examples. Particularly, we construct what Herzberger called “unstable statements with unpredictably complicated variations in truth value.” Besides, we also construct those paradoxes with infinitely many finite primary periods but without any infinite primary period, those with an infinite critical point but without any finite primary period, and so on. This is the first formal appearance of these paradoxes. Our construction demonstrates that the binary sequences generated by a paradoxical sentence are something like genes from which we can even rebuild the original sentence itself.
PubDate: 2022-08-01
- A Unified Logic for Contingency and Accident
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: As shown in Fan (Journal of Philosophical Logic, 48, 425–445, 2019), there are some similarities/resemblances between contingency and accident. Given this, one may naturally ask if we can unify the two operators to manifest all of their similarities/resemblances. In this article, instead of looking at the interactions between the two operators like in Fan (Journal of Philosophical Logic, 48, 425–445, 2019), we turn our attention to the resemblances between the two operators. We extend the unification method in Fan (Logic Journal of the IGPL, 2020) to the current setting. The main results include some model-theoretical ones, such as expressivity, frame definability, bisimulation, and some axiomatization ones.
PubDate: 2022-08-01
- What is a Relevant Connective'
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In this paper, I explore the limits of what a relevant connective is, showing how some basic criteria motivated by the ideology of relevant logicians provide robust limits on potential connectives. These criteria provide some plausible necessary conditions on being a relevant connective.
PubDate: 2022-08-01
- Depth Relevance and Hyperformalism
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result of the paper, we give a very simple proof of a related but strictly stronger result.
PubDate: 2022-08-01
- Arbitrary Public Announcement Logic with Memory
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a natural reduction of the so-called coalition announcement modality to group announcements (in contrast to the memory-free case, where this natural translation was shown to be invalid).
PubDate: 2022-07-20
- Bernoulli Semantics and Ordinal Semantics for Conditionals
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Conditionals with conditional constituents pose challenges for the Thesis, the idea that the probability of a conditional is the corresponding conditional probability. This note is concerned with two proposals for overcoming those challenges, both inspired by early work of van Fraassen: the Bernoulli Semantics associated with Stalnaker and Jeffrey, and augmented with a mechanism for obtaining “local probabilities” by Kaufmann; and a proposal by Bacon which I dub Ordinal Semantics. Despite differences in mathematical details and emphasis of presentation, both proposals lend themselves for use as a basis for a modal-theoretic interpretation of embedded conditionals. The goal of this note is to compare the two frameworks by implementing a model for the interpretation of conditionals in each, based on the same underlying probability model for non-conditional sentences. I show that in the Ordinal model, certain sentences are assigned probabilities that do not accord with intuitions. This problem is familiar from the literature on Bernoulli models and can be addressed by introducing Kaufmann-style local probabilities into Ordinal models. I then show that Bernoulli Semantics has other limitations, in that it assigns probabilities in violation of the Thesis to certain very complex formulas. The upshot is that a fusion of the theories may be our best shot at getting the predictions right.
PubDate: 2022-07-05
- Neighbourhood Semantics for Modal Relevant Logics
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: In this paper, we investigate neighbourhood semantics for modal extensions of relevant logics. In particular, we combine the neighbourhood interpretation of the relevant implication (and related connectives) with a neighbourhood interpretation of modal operators. We prove completeness for a range of systems and investigate the relations between neighbourhood models and relational models, setting out a range of augmentation conditions for the various relations and operations.
PubDate: 2022-06-29
- Monstrous Content and the Bounds of Discourse
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Bounds consequence provides an interpretation of a multiple-conclusion consequence relation in which the derivability of a sequent  is understood as the claim that it is conversationally out-of-bounds to take a position in which each member of Γ is asserted while each member of Δ is denied. Two of the foremost champions of bounds consequence—Greg Restall and David Ripley—have independently indicated that the shape of the bounds in question is determined by conversational practice. In this paper, I suggest that the standard treatments of bounds consequence have focused heavily on the matter of veridicality at the expense of ignoring other features by which conversational bounds are set, prime among them being the matter of content or subject-matter. Furthermore, I argue that the semantic behavior of propositions containing “monstrous” content—content whose introduction is inappropriate to a context independently of veridical considerations—leads to a weak Kleene account of bounds consequence.
PubDate: 2022-06-29
- Mighty Belief Revision
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Belief revision theories standardly endorse a principle of intensionality to the effect that ideal doxastic agents do not discriminate between pieces of information that are equivalent within classical logic. I argue that this principle should be rejected. Its failure, on my view, does not require failures of logical omniscience on the part of the agent, but results from a view of the update as mighty: as encoding what the agent learns might be the case, as well as what must be. The view is motivated by consideration of a puzzle case, obtained by transposing into the context of belief revision a kind of scenario that Kit Fine has used to argue against intensionalism about counterfactuals. Employing the framework of truthmaker semantics, I go on to develop a novel account of belief revision, based on a conception of the update as mighty, which validates natural hyperintensional counterparts of the usual AGM postulates.
PubDate: 2022-06-27
- Subminimal Negation on the Australian Plan
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Frame semantics for negation on the Australian Plan accommodates many different negations, but it falls short on accommodating subminimal negation when the language contains conjunction and disjunction. In this paper, I will present a multi-relational frame semantics –multi-incompatibility frame semantics– that can accommodate subminimal negation. I will first argue that multi-incompatibility frames are in accordance with the philosophical motivations behind negation on the Australian Plan, namely its modal and exclusion-expressing nature. Then, I will prove the soundness and completeness results of a subminimal logic that consists of the multi-incompatibility semantics and a proof system with operational rules that characterize subminimal negation, conjunction and disjunction. Lastly, I will prove some key correspondence theorems that relate frame conditions to certain principles that are associated with stronger negations, which will give rise to a new kite of negations that includes subminimal negation.
PubDate: 2022-06-20
- Probability and Symmetric Logic
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: In this paper we study the interaction between symmetric logic and probability. In particular, we axiomatize the convex hull of the set of evaluations of symmetric logic, yielding the notion of probability in symmetric logic. This answers an open problem of Williams (2016) and Paris (2001).
PubDate: 2022-06-17
- Valuation Semantics for First-Order Logics of Evidence and Truth
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: This paper introduces the logic QLETF, a quantified extension of the logic of evidence and truth LETF, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LETF is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A’s violating some classically valid inferences. The semantics of QLETF combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics.
PubDate: 2022-06-16
- Essence and Necessity
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: What is the relation between metaphysical necessity and essence' This paper defends the view that the relation is one of identity: metaphysical necessity is a special case of essence. My argument consists in showing that the best joint theory of essence and metaphysical necessity is one in which metaphysical necessity is just a special case of essence. The argument is made against the backdrop of a novel, higher-order logic of essence (HLE), whose core features are introduced in the first part of the paper. The second part investigates the relation between metaphysical necessity and essence in the context of HLE. Reductive hypotheses are among the most natural hypotheses to be explored in the context of HLE. But they also have to be weighed against their non-reductive rivals. I investigate three different reductive hypotheses and argue that two of them fare better than their non-reductive rivals: they are simpler, more natural, and more systematic. Specifically, I argue that one candidate reduction, according to which metaphysical necessity is truth in virtue of the nature of all propositions, is superior to the others, including one proposed by Kit Fine, according to which metaphysical necessity is truth in virtue of the nature of all objects. The paper concludes by offering some reasons to think that the best joint theory of essence and metaphysical necessity is one in which the logic of metaphysical necessity includes S4, but not S5.
PubDate: 2022-06-01
DOI: 10.1007/s10992-021-09646-0
- A General Theory of Location Based on the Notion of Entire Location
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: It would be a good thing to have at our disposal a general theory of location that is neutral with respect to (i.e. that does not rule out or entail) (i) the view that some objects have more than one exact location, (ii) the view that some objects are located without having an exact location, and (iii) the view that some objects are “spanners”—where a spanner is an object exactly located at a region that has proper parts but which has no proper part exactly located at a proper part of the region. As far as I know, no theory of location that can be found in the literature has this feature. I put forward a new theory that does—or so I argue. The theory takes as its sole locational primitive the notion of being entirely located at.
PubDate: 2022-06-01
DOI: 10.1007/s10992-021-09641-5
- Neighbourhood Semantics for Quantified Relevant Logics
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: The Mares-Goldblatt semantics for quantified relevant logics have been developed for first-order extensions of R, and a range of other relevant logics and modal extensions thereof. All such work has taken place in the the ternary relation semantic framework, most famously developed by Sylvan (née Routley) and Meyer. In this paper, the Mares-Goldblatt technique for the interpretation of quantifiers is adapted to the more general neighbourhood semantic framework, developed by Sylvan, Meyer, and, more recently, Goble. This more algebraic semantics allows one to characterise a still wider range of logics, and provides the grist for some new results. To showcase this, we show, using some non-augmented models, that some quantified relevant logics are not conservatively extended by connectives the addition of which do conservatively extend the associated propositional logics, namely fusion and the dual implication. We close by proposing some further uses to which the neighbourhood Mares-Goldblatt semantics may be put.
PubDate: 2022-06-01
DOI: 10.1007/s10992-021-09637-1
- Higher-Order Logic and Disquotational Truth
-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification.
PubDate: 2022-05-07
DOI: 10.1007/s10992-022-09654-8
- Corrections to: Natural Deduction for the Sheffer Stroke and Peirce’s
Arrow (and any Other Truth-Functional Connective)-
Free pre-print version: Loading...
Rate this result:
What is this?
Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: A Correction to this paper has been published: https://doi.org/10.1007/s10992-022-09665-5
PubDate: 2022-05-02
DOI: 10.1007/s10992-022-09665-5
|
Hybrid journal (It can contain Open Access articles)
