The aim of this paper is to introduce the logics $$\textit{FFDE}$$ and $$\textit{FN}{4}$$, which are universally free versions of Belnap-Dunn’s four-valued logic, also known as the logic of first-degree entailment ( $$\textit{FDE}$$ ), and Nelson’s paraconsistent logic $$N^{-}$$ (a.k.a. $$Q\!N {4}$$ ). Both $$\textit{FDE}$$ and $$Q\!N {4}$$ are suitable to be interpreted as information-based logics, that is, logics that are capable of representing the deductive behavior of possibly inconsistent and incomplete information in a database. Like $$Q\!N {4}$$ and some non-free (...) first-order extensions of $$\textit{FDE}$$, $$\textit{FFDE}$$ and $$\textit{FN}{4}$$ are endowed with Kripke-style variable domain semantics, which allows representing the dynamic aspect of information processing, that is, how a database receives new information over time, including information about new individuals. We argue, however, that $$\textit{FFDE}$$ and $$\textit{FN}{4}$$ can better represent the development of inconsistent and incomplete information states (i.e., configurations of a database) over time than their non-free versions. First, because they allow for empty domains, which corresponds to the idea that a database may acknowledge no individual at all at an early stage of its development. Second, because they allow for empty names, which get interpreted as information about new individuals is inserted into the database. Also, both systems include an identity predicate that is interpreted along the same lines of the other logical operators, viz., in terms of independent positive and negative rules. (shrink)

The aim of this paper is to introduce the logics \(\textit{FFDE}\) and \(\textit{FN}{4}\), which are universally free versions of Belnap-Dunn’s four-valued logic, also known as the logic of first-degree entailment ( \(\textit{FDE}\) ), and Nelson’s paraconsistent logic \(N^{-}\) (a.k.a. \(Q\!N {4}\) ). Both \(\textit{FDE}\) and \(Q\!N {4}\) are suitable to be interpreted as information-based logics, that is, logics that are capable of representing the deductive behavior of possibly inconsistent and incomplete information in a database. Like \(Q\!N {4}\) and some non-free (...) first-order extensions of \(\textit{FDE}\), \(\textit{FFDE}\) and \(\textit{FN}{4}\) are endowed with Kripke-style variable domain semantics, which allows representing the dynamic aspect of information processing, that is, how a database receives new information over time, including information about new individuals. We argue, however, that \(\textit{FFDE}\) and \(\textit{FN}{4}\) can better represent the development of inconsistent and incomplete information states (i.e., configurations of a database) over time than their non-free versions. First, because they allow for empty domains, which corresponds to the idea that a database may acknowledge no individual at all at an early stage of its development. Second, because they allow for empty names, which get interpreted as information about new individuals is inserted into the database. Also, both systems include an identity predicate that is interpreted along the same lines of the other logical operators, viz., in terms of independent positive and negative rules. (shrink)

Some learning strategies that work well when computational considerations are abstracted away from become severely limiting when such considerations are taken into account. We illustrate this phenomenon for agents who attempt to extrapolate patterns in binary data streams chosen from among a countable family of possibilities. If computational constraints are ignored, then two strategies that will always work are learning by enumeration (enumerate the possibilities—in order of simplicity, say—then search for the one earliest in the ordering that agrees with your (...) data and use it to predict the next data point) and Bayesian learning. But there are many families of computable data streams that, although they can be successfully extrapolated by computable agents, cannot be handled by any computable learner by enumeration. And while there is a sense in which Bayesian learning is a fully general strategy for computable learners, the ability to mimic powerful learners comes at a price for Bayesians: they cannot, in general, become highly confident of their predictions in the limit of large data sets and they cannot, in general, use priors that incorporate all relevant background knowledge. (shrink)

I distinguish between instantial sentences (_There are elephants that swim_), particular quantification, and predication of existence in natural language. I explore the logical relation between the first two, while the last one is shown independent of either. I continue to consider the incorporation of the three kinds of sentence in the Quantified Argument Calculus (Quarc). I provide formalisations that preserve the logical relations specified earlier. I also extend the analysis to quantified instantial sentences (_There are_ five _elephants that swim_) and (...) modal ones. A conclusion of this work is that quantification and instantial sentences provide no guide to ontology. (shrink)

The concept of location—of something being located at, or occupying, a region or a place—has been an important topic of philosophical investigation over the past fifteen years or so. Yet all the theories of location that have been put forward so far are unsatisfactory, because they fail to have the conceptual resources to describe certain basic locational phenomena. I introduce and partly develop a novel theory of location that does better in this respect than its predecessors. Its most distinctive feature (...) is the way in which it handles so-called cases of multilocation: according to the theory, objects capable of being multilocated occupy regions via proxies, and—in a slogan, and very roughly—to be multilocated is to have several proxies located at different regions. (shrink)

The concept of location—of something being located at, or occupying, a region or a place—has been an important topic of philosophical investigation over the past fifteen years or so. Yet all the theories of location that have been put forward so far are unsatisfactory, because they fail to have the conceptual resources to describe certain basic locational phenomena. I introduce and partly develop a novel theory of location that does better in this respect than its predecessors. Its most distinctive feature (...) is the way in which it handles so-called cases of _multilocation_: according to the theory, objects capable of being multilocated occupy regions via _proxies_, and—in a slogan, and very roughly—to be multilocated is to have several proxies located at different regions. (shrink)

We use the normality framework of Goodman and Salow (2018, 2021, 2023b) to investigate of dynamics of rational belief. The guiding idea is that people are entitled to believe that their circumstances aren’t especially abnormal. More precisely, a rational agent’s beliefs rule out all and only those possibilities that are either (i) ruled out by their evidence or (ii) sufficiently less normal than some other possibility not ruled out by their evidence. Working within this framework, we argue that the logic (...) of rational belief revision is much weaker than is usually supposed. We do so by isolating a natural family of orthodox principles about belief revision, describing realistic cases in which these principles seem to fail, and showing how these counterexamples are predicted by independently motivated models of the cases in question. In these models, whether one evidential possibility counts as sufficiently less normal than another is determined by underlying probabilities (together with a contextually determined question). We argue that the resulting probabilistic account of belief compares favorably with other such accounts, including Lockeanism (Foley, 1993), a ‘stability’ account inspired by Leitgeb (2017), the ‘tracking theory’ of Lin and Kelly (2012), and the influential precursor of Levi (1967). We show that all of these accounts yield subtly different but similarly heterodox logics of belief revision. (shrink)

Incurvati and Schlöder (_Journal of Philosophical Logic, 51_(6), 1549–1582, 2022) have recently proposed to define supervaluationist logic in a multilateral framework, and claimed that this defuses well-known objections concerning supervaluationism’s apparent departures from classical logic. However, we note that the unconventional multilateral syntax prevents a straightforward comparison of inference rules of different levels, across multi- and unilateral languages. This leaves it unclear how the supervaluationist multilateral logics actually relate to classical logic, and raises questions about Incurvati and Schlöder’s response to (...) the objections. We overcome the obstacle, by developing a general method for comparisons of strength between multi- and unilateral logics. We apply it to establish precisely on which inferential levels the supervaluationist multilateral logics defined by Incurvati and Schlöder are classical. Furthermore, we prove general limits on how classical a multilateral logic can be while remaining supervaluationistically acceptable. Multilateral supervaluationism leads to sentential logic being classical on the levels of theorems and regular inferences, but necessarily strictly weaker on meta- and higher-levels, while in a first-order language with identity, even some classical theorems and inferences must be forfeited. Moreover, the results allow us to fill in the gaps of Incurvati and Schlöder’s strategy for defusing the relevant objections. (shrink)

Incurvati and Schlöder (Journal of Philosophical Logic, 51(6), 1549–1582, 2022) have recently proposed to define supervaluationist logic in a multilateral framework, and claimed that this defuses well-known objections concerning supervaluationism’s apparent departures from classical logic. However, we note that the unconventional multilateral syntax prevents a straightforward comparison of inference rules of different levels, across multi- and unilateral languages. This leaves it unclear how the supervaluationist multilateral logics actually relate to classical logic, and raises questions about Incurvati and Schlöder’s response to (...) the objections. We overcome the obstacle, by developing a general method for comparisons of strength between multi- and unilateral logics. We apply it to establish precisely on which inferential levels the supervaluationist multilateral logics defined by Incurvati and Schlöder are classical. Furthermore, we prove general limits on how classical a multilateral logic can be while remaining supervaluationistically acceptable. Multilateral supervaluationism leads to sentential logic being classical on the levels of theorems and regular inferences, but necessarily strictly weaker on meta- and higher-levels, while in a first-order language with identity, even some classical theorems and inferences must be forfeited. Moreover, the results allow us to fill in the gaps of Incurvati and Schlöder’s strategy for defusing the relevant objections. (shrink)

In the paper, we consider a particular way of obtaining modal extensions of the discussive logic \({\textbf {D}} _{{\textbf {2}} }\) (Jaśkowski 1948 ; 1949 ). The proposed framework of defining modal discussive logics is a novelty compared to the one presented in Mruczek-Nasieniewska et al. ( 2019 _Logic Journal of IGPL, 27_(4), 451–477). In this case, different discussants may have different views about what is necessary (resp. possible) in a given world. We enrich the intuitive model of discussion given (...) by Jaśkowski. This is obtained by considering two-sorted frames. The first sort consists of discussants and the second of situations. We have a universal accessibility relation between the discussants, i.e., we use the standard semantic formulation of \({\textbf {S5}} \), which is characteristic of the original variant of the discussive logic \({\textbf {D}} _{{\textbf {2}} }\). For a frame, a valuation assigns to each discussant a set of atomic sentences they accept in a given situation. Although different discussants may have different views about what occurs in a given world, their views should be within the same “domain of possibilities”. Therefore, we have a common set of possible situations and an accessibility relation for all discussants. The introduction of modal operators allows for specifying strict discussive implications, which—as it seems—correspond to colloquial discussive conditionals better than Jaśkowski’s discussive implication. We also analyze various semantic and syntactic (including axiomatizations) aspects of modal discussive logics resulting from the proposed framework. (shrink)

In the paper, we consider a particular way of obtaining modal extensions of the discussive logic $${\textbf {D}} _{{\textbf {2}} }$$ (Jaśkowski 1948; 1949). The proposed framework of defining modal discussive logics is a novelty compared to the one presented in Mruczek-Nasieniewska et al. (2019Logic Journal of IGPL, 27(4), 451–477). In this case, different discussants may have different views about what is necessary (resp. possible) in a given world. We enrich the intuitive model of discussion given by Jaśkowski. This is (...) obtained by considering two-sorted frames. The first sort consists of discussants and the second of situations. We have a universal accessibility relation between the discussants, i.e., we use the standard semantic formulation of $${\textbf {S5}} $$, which is characteristic of the original variant of the discussive logic $${\textbf {D}} _{{\textbf {2}} }$$. For a frame, a valuation assigns to each discussant a set of atomic sentences they accept in a given situation. Although different discussants may have different views about what occurs in a given world, their views should be within the same “domain of possibilities”. Therefore, we have a common set of possible situations and an accessibility relation for all discussants. The introduction of modal operators allows for specifying strict discussive implications, which—as it seems—correspond to colloquial discussive conditionals better than Jaśkowski’s discussive implication. We also analyze various semantic and syntactic (including axiomatizations) aspects of modal discussive logics resulting from the proposed framework. (shrink)

In the metaphysics of modality, one finds a distinction between two families of modalities: the so-called ‘objective’, ‘real’ or ‘circumstantial’ modalities and the ‘non-objective’, ‘non-real’ or ‘non-circumstantial’ modalities. The guiding thought is that in some intuitive sense the former modalities pertain to contingency in worldly circumstance—how things could have genuinely otherwise been—whereas the latter do not. Moreover the distinction has acquired importance through attempts to elucidate the modality of metaphysical necessity by assigning it a distinctive role within the objective modalities. (...) In this paper I use the resources of higher-order modal logic to explore how one might systematize these ideas. I present a formal tension which shows that one natural way of systematizing them is unstable. And whilst I show that there are ways of stabilizing the guiding picture, even the best of them involves deeply non-trivial departures from how that picture is ordinarily understood. I conclude by revisiting the motivation for the underlying picture of modalities. (shrink)

In the metaphysics of modality, one finds a distinction between two families of modalities: the so-called ‘objective’, ‘real’ or ‘circumstantial’ modalities and the ‘non-objective’, ‘non-real’ or ‘non-circumstantial’ modalities. The guiding thought is that in some intuitive sense the former modalities pertain to contingency in worldly circumstance—how things could have genuinely otherwise been—whereas the latter do not. Moreover the distinction has acquired importance through attempts to elucidate the modality of metaphysical necessity by assigning it a distinctive role within the objective modalities. (...) In this paper I use the resources of higher-order modal logic to explore how one might systematize these ideas. I present a formal tension which shows that one natural way of systematizing them is unstable. And whilst I show that there are ways of stabilizing the guiding picture, even the best of them involves deeply non-trivial departures from how that picture is ordinarily understood. I conclude by revisiting the motivation for the underlying picture of modalities. (shrink)