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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.

Authors:LIN; HANTI Pages: 277 - 310 Abstract: Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is enumerative induction in its full strength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. PubDate: 2022-01-03 DOI: 10.1017/S1755020321000605

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Authors:MEISSNER; SILKE, OTTO, MARTIN Pages: 311 - 333 Abstract: We present a natural standard translation of inquisitive modal logic into first-order logic over the natural two-sorted relational representations of the intended models, which captures the built-in higher-order features of . This translation is based on a graded notion of flatness that ties the inherent second-order, team-semantic features of over information states to subsets or tuples of bounded size. A natural notion of pseudo-models, which relaxes the non-elementary constraints on the intended models, gives rise to an elementary, purely model-theoretic proof of the compactness property for . Moreover, we prove a Hennessy-Milner theorem for , which crucially uses -saturated pseudo-models and the new standard translation. As corollaries we also obtain van Benthem style characterisation theorems. PubDate: 2021-08-31 DOI: 10.1017/S175502032100037X

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Authors:MADARÁSZ; JUDIT X., STANNETT, MIKE, SZÉKELY, GERGELY Pages: 334 - 361 Abstract: In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle, and he demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, and convert his basic background assumptions into explicit axioms. Instead of assuming that the structure of physical quantities is the field of real numbers, we assume only that they form an ordered field. This allows us to investigate how Borisov’s theorem depends on the structure of quantities.We demonstrate (as our main contribution) how to construct Euclidean, Galilean, and Poincaré models of Borisov’s axiom system over every non-Archimedean field. We also demonstrate the existence of an infinite descending chain of models and transformation groups in each of these three cases, something that is not possible over Archimedean fields.As an application, we note that there is a model of Borisov’s axioms that satisfies the relativity principle, and in which the worldview transformations are Euclidean isometries. Over the field of reals it is easy to eliminate this model using natural axioms concerning time’s arrow and the absence of instantaneous motion. In the case of non-Archimedean fields, however, the Euclidean isometries appear intrinsically as worldview transformations in models of Borisov’s axioms, and neither the assumption of time’s arrow, nor the rejection of instantaneous motion, can eliminate them. PubDate: 2021-03-23 DOI: 10.1017/S1755020321000149

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Authors:FERVARI; RAUL, VELÁZQUEZ-QUESADA, FERNANDO R., WANG, YANJING Pages: 450 - 486 Abstract: As a new type of epistemic logics, the logics of knowing how capture the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work on these logics focuses on axiomatizations; this paper makes the first study of their model theoretical properties. It does so by introducing suitable notions of bisimulation for a family of five knowing how logics based on different notions of plans. As an application, we study and compare the expressive power of these logics. PubDate: 2021-03-22 DOI: 10.1017/S1755020321000101

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Authors:CANAVOTTO; ILARIA, BERTO, FRANCESCO, GIORDANI, ALESSANDRO Pages: 362 - 387 Abstract: We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity' How can we gain new knowledge via it' What is voluntary in it and what is not' We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization. PubDate: 2020-06-29 DOI: 10.1017/S1755020320000039

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Authors:GARAPA; MARCO Pages: 388 - 408 Abstract: In this paper, we propose a new kind of nonprioritized operator which we call two level credibility-limited revision. When revising through a two level credibility-limited revision there are two levels of credibility and one of incredibility. When revising by a sentence at the highest level of credibility, the operator behaves as a standard revision, if the sentence is at the second level of credibility, then the outcome of the revision process coincides with a standard contraction by the negation of that sentence. If the sentence is not credible, then the original belief set remains unchanged. In this article, we axiomatically characterize several classes of two level credibility-limited revision operators. PubDate: 2020-07-21 DOI: 10.1017/S1755020320000283

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Authors:BADIA; GUILLERMO, CINTULA, PETR, HÁJEK, PETR, TEDDER, ANDREW Pages: 487 - 504 Abstract: In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory' It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much weaker arithmetic theory, a version of Robinson’s R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic. PubDate: 2020-06-29 DOI: 10.1017/S175502032000012X

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Authors:INCURVATI; LUCA, SCHLÖDER, JULIAN J. Pages: 505 - 536 Abstract: We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati & Schlöder, 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic modulo an appropriate translation. The logical framework developed provides the basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve. PubDate: 2020-07-21 DOI: 10.1017/S1755020320000313

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Authors:PARLAMENTO; FRANCO, PREVIALE, FLAVIO Pages: 537 - 551 Abstract: We show that the replacement rule of the sequent calculi in [8] can be replaced by the simpler rule in which one of the principal formulae is not repeated in the premiss. PubDate: 2020-07-02 DOI: 10.1017/S1755020320000155

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Authors:HAMAMI; YACIN Pages: 409 - 449 Abstract: Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowledge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous' According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary mathematicians, and is endorsed by many logicians and philosophers, but it has also been heavily criticized in the philosophy of mathematics literature. Progress on the debate between the proponents and opponents of the standard view is, however, currently blocked by a major obstacle, namely, the absence of a precise formulation of it. To remedy this deficiency, I undertake in this paper to provide a precise formulation and a thorough evaluation of the standard view of mathematical rigor. The upshot of this study is that the standard view is more robust to criticisms than it transpires from the various arguments advanced against it, but that it also requires a certain conception of how mathematical proofs are judged to be rigorous in mathematical practice, a conception that can be challenged on empirical grounds by exhibiting rigor judgments of mathematical proofs in mathematical practice conflicting with it. PubDate: 2019-10-04 DOI: 10.1017/S1755020319000443