Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...) connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. (shrink)

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. (shrink)

We propose a logic of imagination, based on simulated belief revision, that intends to uncover the logical patterns governing the development of imagination in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises the algorithm that specifies what goes on in between receiving a certain input for an imaginative episode and what is imagined in the resulting imagination, as well as the goal-orientedness of imagination, by allowing the context to determine, what we call, (...) the overall topic of the imaginative episode. To achieve this, we employ well-developed tools and techniques from dynamic epistemic logic and belief revision theory, enriched with a topicality component which has been exploited in the recent literature. As a result, our logic models a great number of cognitive theories of pretense and imagination [cf. Currie and Ravenscroft ; Nichols and Stich ; Byrne ; Williamson ; Langland-Hassan Knowledge through imaginaion, Oxford University Press, Oxford, 2016]. (shrink)

We propose a new topological semantics for evidence, evidence-based justifications, belief, and knowledge. Resting on the assumption that an agent’s rational belief is based on the available evidence, we try to unveil the concrete relationship between an agent’s evidence, belief, and knowledge via a rich formal framework afforded by topologically interpreted modal logics. We prove soundness, completeness, decidability, and the finite model property for the associated logics, and apply this setting to analyze key epistemological issues such as “no false lemma” (...) Gettier examples, misleading defeaters, undefeated justification versus undefeated belief, as well as the defeasibility theories of knowledge. (shrink)

The received view says that possibility is the dual of necessity: a proposition is (metaphysically, logically, epistemically etc.) possible iff it is not the case that its negation is (metaphysically, logically, epistemically etc., respectively) necessary. This reading is usually taken for granted by modal logicians and indeed seems plausible when dealing with logical or metaphysical possibility. But what about epistemic possibility? We argue that the dual definition of epistemic possibility in terms of epistemic necessity generates tension when reasoning about non-idealized (...) agents and is a problem of concern for most hyperintensional epistemic logics that alleviate the problem of logical omniscience. The tension is particularly evident when knowledge is taken as a primitive to define other epistemic concepts, such as justification and belief, as done in the knowledge-first tradition. We propose a non-dual interpretation of epistemic possibility, employing a hyperintensionality filter similar to the one that makes the corresponding epistemic necessity operator hyperintensional. We employ the proposed semantics to model Stalnaker's belief as epistemic possibility of knowledge and provide a sound and complete axiomatization for a hyperintensional version of his bimodal logic of knowledge and belief. (shrink)

Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit the assumptions discharged in (...) propositional proofs, thereby expressing blueprints for proofs. A natural deduction system is provided that permits to reason about and manage such proof blueprints. (shrink)

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...) with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

Justification logics provide frameworks for studying the fine structure of evidence and justification. Traditionally, these logics do not impose any closure requirements on justification. In this paper, we argue that for some applications they should subject justification to closure under some variety of logical consequence. Specifically, we argue, building on ideas from Beall, that the non-classical logic FDE offers a particularly attractive notion of consequence for this purpose and define a justification logic where justification is closed under FDE consequence. We (...) show the resulting logic to be sound and complete. Lastly, we discuss how the closure of justification under FDE ontrasts closure under related non-classical logics and how our approach contrasts with some alternatives. (shrink)

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (shrink)

In frameworks in which _topic-__theoretic_ considerations—_e.g._, tracking _subject-matter_ or _topic_—are given equal importance with _veridical_ considerations, assigning topics to formulae in a satisfactory way is of critical importance. While intuitions are more-or-less solid for _extensional_ formulae in a propositional language, arriving at a compelling account of the subject-matter of _intensional_ formulae, _i.e._, formulae including intensional operators, is more challenging. This paper continues previous work on modeling topics of intensional formulae in William Parry’s logic of analytic implication, adapting the general techniques (...) to the framework of _topic-sensitive intentional modals_ (TSIMs) championed by Francesco Berto and his collaborators. As illustrations, we introduce variations on Berto and Peter Hawke’s logic of knowability relative to information ( \(\pmb {\textsf{KRI}}\) ), including a refinement sensitive to topic-theoretic distinctions between knowledge and belief and a refinement capable of internalizing its own properties. Finally, subsystems of Aybüke Ozgun and Berto’s logic of plain hyperintensional belief ( \(\pmb {\textsf{PHB}}\) ) are introduced in which fine-grained distinctions in subject-matter are possible. (shrink)

In his Knowledge and Belief (1962), Hintikka establishes his system of epistemic logic with the KK (Knowing that One Knows, in symbols, Kp→KKp) principle (KK for short). However, his system of epistemic logic and the KK principle are grounded upon his strong notion of knowledge, which requires that knowledge is infallible, that is, it makes further inquiry pointless, and becomes ‘discussion-stopper’; knowledge implies truth, to wit, cognitive agents will not be mistaken in their knowledge; cognitive agents will be ‘perfect logicians’, (...) i.e. they have infinitive capability of logical inference. Hintikka calls the argument for KK from the strong notion of knowledge as the ‘transcendental argument’ for KK. Obviously, the strong notion of knowledge is far away from our ordinary conception of knowledge; based on such a strong sense of knowledge, epistemic logic has met the problem of logical omnipotence, and is difficult to apply in our ordinary cognitive practice. Moreover, there is no close connection of the KK principle with internalism or externalism. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)