Explore the vast range of titles available.

“The Craft of Formal Logic” is Arthur Prior’s unpublished textbook, written in 1950–51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of ‘entities’ with modal character. Although he talks about these ‘entities’ only informally, and hesitates how to name them, using alternately the phrases ‘possible states of affairs’, ‘chances’, ‘cases’ or ‘peculiar objects’, he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of “The Craft” with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality.

Pictorial free perception reports are sequences in comics or film of one unit that depicts an agent who is looking, and a following unit that depicts what they see. This paper proposes an analysis in possible worlds semantics and event semantics of such sequences. Free perception sequences are implicitly anaphoric, since the interpretation of the second unit refers to the agent depicted in the first. They are argued to be possibly non-extensional, because they can depict hallucination or mis-perception. The semantics proposed here employs an account of anaphora using discourse referents, a formalized possible worlds semantics for pictorial narratives, and, to model the epistemic consequences of perceptual events, the event alternative construction from dynamic epistemic logic. In intensional examples, the second unit depicting what is seen is analyzed as embedded. It is argued that a semantics for embedding where the attitudinal state of the depicted agent is required to entail the semantic content of the picture attributes too much information to the agent. This is addressed with a model of normal looking, and a semantics for the embedding construction that uses existential quantification over alternatives, rather than universal quantification.

We present a logic of evidence that reduces agents’ epistemic idealisations by combining classical propositional logic with substructural modal logic for formulas in the scope of epistemic modalities. To this aim, we provide a neighborhood semantics of evidence, which provides a modal extension of Fine’s semantics for relevant propositional logic. Possible worlds semantics for classical propositional logic is then obtained by defining the set of possible worlds as a special subset of information states in Fine’s semantics. Finally, we prove that evidence is a hyperintensional and non-prime notion in our logic, and provide a sound and complete axiomatisation of our evidence logic.

Przedmiotem niniejszego artykułu jest formalna analiza systemu C2 logiki okresów warunkowych Roberta Stalnakera. We wstępnej, pierwszej części pracy pokazano w ogólności, że ujęcie zdania warunkowego z języka naturalnego za pomocą takich spójników logicznych, jak implikacja materialna czy ścisła implikacja Lewisa, nie jest w pełni adekwatne. Część druga została w całości poświęcona szczegółowej analizie systemu C2. Czytelnik znajdzie w niej dowody głównych tez i własności systemu C2, a także formalne przedstawienie semantyki dla bezkwantyfikatorowej wersji tego systemu. W części trzeciej omówione zostały podstawowe argumenty przeciwko „sztandarowej” tezie Stalnakera: tezie (CEM) o tzw. warunkowym wyłączonym środku (ang. Conditional Excluded Middle). Poddane krytyce zostały także stosowane przez Stalnakera rozwiązania semantyczne.

A hyperintensional epistemic logic would take the contents which can be known or believed as more fine-grained than sets of possible worlds. I consider one objection to the idea: Williamson’s Objection from Overfitting. I propose a hyperintensional account of propositions as sets of worlds enriched with topics: what those propositions, and so the attitudes having them as contents, are about. I show that the account captures the conditions under which sentences express the same content; that it can be pervasively applied in formal and mainstream epistemology; and that it is left unscathed by the objection.

The present paper studies formal properties of so-called modal information logics (MILs)—modal logics first proposed in (van Benthem 1996 ) as a way of using possible-worlds semantics to model a theory of information. They do so by extending the language of propositional logic with a binary modality defined in terms of being the supremum of two states. First proposed in 1996, MILs have been around for some time, yet not much is known: (van Benthem 2017 , 2019 ) pose two central open problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability. The main results of the first part of this paper are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability. In the proof of the latter, an emphasis is put on the method applied as a heuristic for proving decidability ‘via completeness’ for semantically introduced logics; the logics lack the FMP w.r.t. their classes of definition, but not w.r.t. a generalized class. These results are build upon to axiomatize and prove decidable the MILs attained by endowing the language with an ‘informational implication’—in doing so a link is also made to the work of (Buszkowski 2021 ) on the Lambek Calculus.

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke's new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics.

Charles Peirce developed Existential Graphs as a diagrammatic syntax for representing and reasoning about propositions, with three parts: Alpha for propositional logic, Beta for first-order predicate logic, and Gamma for aspects of modal logic, second-order logic, and metalanguage. He made several adjustments between 1909 and 1911 that merit further consideration: using heavy lines to denote possible states of things in which attached propositions would be true, drawing a red line just inside the edge of a page and writing postulates in the resulting margin, shading oddly enclosed areas instead of drawing thin lines as their boundaries, and using multiple sheets of paper to represent different subjects within the overall universe of discourse. These modifications can be combined to constitute a plausible candidate for Delta, a fourth part that Peirce intended to add but never spelled out. It implements modern formal systems of modal propositional logic in accordance with a version of possible worlds semantics in which the laws for the actual state of things are facts in every possible state of things.

Possible-worlds accounts of mental or linguistic content are often criticized for being too coarse-grained. To make room for more fine-grained distinctions among contents, several authors have recently proposed extending the space of possible worlds by 'impossible worlds'. We argue that this strategy comes with serious costs: we would effectively have to abandon most of the features that make the possible-worlds framework attractive. More generally, we argue that while there are intuitive and theoretical considerations against overly coarse-grained notions of content, the same kinds of considerations also prohibit an overly fine-grained individuation of content. An adequate notion of content, it seems, should have intermediate granularity. However, it is hard to construe a notion of content that meets these demands. Any notion of content, we suggest, must be either implausibly coarse-grained or implausibly fine-grained (or both).

In this paper, we propose a unified account of conditionals inspired by Frank Ramsey. Most contemporary philosophers agree that Ramsey’s account applies to indicative conditionals only. We observe against this orthodoxy that his account covers subjunctive conditionals as well—including counterfactuals. In light of this observation, we argue that Ramsey’s account of conditionals resembles Robert Stalnaker’s possible worlds semantics supplemented by a model of belief. The resemblance suggests to reinterpret the notion of conditional degree of belief in order to overcome a tension in Ramsey’s account. The result of the reinterpretation is a tenable account of conditionals that covers indicative and subjunctive as well as qualitative and probabilistic conditionals.