In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a (...) wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic. (shrink)

This paper presents a short survey of recent developments in stit theories, with an emphasis on combinations of stit and deontic logic, and those of stit and epistemic logic.

This paper works within a particular framework for reasoning about actions—sometimes known as the framework of “stit semantics”—originally due to Belnap and Perloff, based ultimately on the theory of indeterminism set out in Prior’s indeterministic tense logic, and developed in full detail by Belnap, Perloff, and Xu [3]. The issues I want to consider arise when certain normative, or decision theoretic, notions are introduced into this framework: here I will focus on the notion of a right action, and so on (...) the formulation of act utilitarianism within this indeterministic setting. The problem is simply that there are two different, and conflicting, ways of defining this notion, both well-motivated, and both carrying intuitive weight. (shrink)

Some intuitive normative principles raise vexing 'detaching problems' by their failure to license modus ponens. I examine three such principles (a self-reliance principle and two different instrumental principles) and recent stategies employed to resolve their detaching problems. I show that solving these problems necessitates postulating an indefinitely large number of senses for 'ought'. The semantics for 'ought' that is standard in linguistics offers a unifying strategy for solving these problems, but I argue that an alternative approach combining an end-relational theory (...) of normativity with a comparative probabilistic semantics for 'ought' provides a more satisfactory solution. (shrink)

Let us say that a normative conflict is a situation in which an agent ought to perform an action A, and also ought to perform an action B, but in which it is impossible for the agent to perform both A and B. Not all normative conflicts are moral conflicts, of course. It may be that the agent ought to perform the action A for reasons of personal generosity, but ought to perform the action B for reasons of prudence: perhaps (...) A involves buying a lavish gift for a friend, while B involves depositing a certain amount of money in the bank. In general, our practical deliberation is shaped by a concern with a variety of morally neutral goods—not just generosity and prudence, but any number of others, such as etiquette, aesthetics, fun—many of which are capable of providing conflicting reasons for action. I mention these ancillary values in the present setting, however, only to put them aside. We will be concerned here, not with normative conflicts more generally, but precisely with moral conflicts—situations in which, even when our attention is restricted entirely to moral reasons for action, it is nevertheless true that an agent ought to do A and ought to do B, where it is impossible to do both. (shrink)

The article puts forward a branching-style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of equations, one based on mappings (...) between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping- and the equations-based approaches. After giving a detailed formal explication of a branching-based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching- and the mapping-based approach. We conclude that the branching-based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories. 1 Introduction2 Determinism in Philosophy of Science: Three Approaches2.1 Determinism: The core idea and how to spell it out2.2 The three approaches in more detail2.3 Representing indeterminism3 Orthodoxy: DMAP, with Invocations of DEQN4 Branching-Style Determinism 4.1 Models and realizations4.2 Faithfulness4.3 Two types of branching topologies 5 Comparing the Approaches5.1 Case studies5.2 Formal comparison of the DMAP and DBRN frameworks6 Conclusions. (shrink)

I present a variant of with time, called, interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: the future tense and past tense operators, and the operator of group agency for the grand coalition. A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment.

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison between (...) the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT by Belnap and colleagues. (shrink)

The communication process is analysed on the basis of the notions of trust and agency. The aim of the paper is to clarify the role played by causality on the one hand and the role played by logical consequences of assumptions about trust in information sources on the other hand. The first part is informal and the second part refers to the logical framework of modal logic though it requires a quite limited background in this area.

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996 ) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza ( 1989 ) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...) obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. -/- I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis' V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. -/- My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like "If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated" is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations. (shrink)

Ever since John Locke, philosophers have discussed the possibility of a normative epistemology: are there epistemic obligations binding the cognitive economy of belief and disbelief? Locke's influential answer was evidentialist: we have an epistemic obligation to believe in accordance with our evidence. In this dissertation, I place the contemporary literature on agency and reasons at the service of some such normative epistemology. I discuss the semantics of obligations, the connection between obligations and reasons to believe, the implausibility of Lockean evidentialism, (...) and some of the alleged connections between agency and justification. (shrink)