Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...) I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

The received wisdom on ability modals is that they differ from their epistemic and deontic cousins in what inferences they license and better receive a universal or conditional analysis instead of an existential one. The goal of this paper is to sharpen the empirical picture about the semantics of ability modals, and to propose an analysis that explains what makes the can of ability so special but that also preserves the crucial idea that all uses of can share a common (...) lexical semantics. The resulting framework combines tools and techniques from dynamic and inquisitive semantics with insights from the literature of the role of agency in deontic logic. It explains not only why the can of ability, while essentially being an existential modal operator, sometimes resists distribution over disjunction and interacts with its duals in particular and hitherto unnoticed ways, but also has a tendency to license free choice inferences. (shrink)

Recent theories of agency (sees to it that) of Nuel Belnap and Michael Perloff are examined, particularly in the context of an early proposal of the author.

A history of the logic of action is outlined, beginning with St Anselm. Five modern authors are discussed in some detail: von Wright, Fitch, Kanger, Chellas and Pratt.

The Free Choice effect—whereby \\) seems to entail both \ and \—has traditionally been characterized as a phenomenon affecting the deontic modal ‘may’. This paper presents an extension of the semantic account of free choice defended by Fusco to the agentive modal ‘can’, the ‘can’ which, intuitively, describes an agent’s powers. On this account, free choice is a nonspecific de re phenomenon that—unlike typical cases—affects disjunction. I begin by sketching a model of inexact ability, which grounds a modal approach to (...) agency in a Williamson -style margin of error. A classical propositional semantics combined with this framework can reflect the intuitions highlighted by Kenny ’s dartboard cases, as well as the counterexamples to simple conditional views recently discussed by Mandelkern et al.. In Section 3, I turn to an independently motivated actual-world-sensitive account of disjunction, and show how it extends free choice inferences into an object language for propositional modal logic. (shrink)

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...) is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT. (shrink)

Based on a notion of "companions to stit formulas" applied in other papers dealing with astit logics, we introduce "choice formulas" and "nested choice formulas" to prove the completeness theorems for dstit logics in a language with the dstit operator as the only non-truth-functional operator. The main logic discussed in this paper is the basic logic of dstit with multiple agents, other logics discussed include the basic logic of dstit with a single agent and some logics of dstit with multiple (...) agents each of which corresponds to a semantic condition concerning the number of possible choices for agents. (shrink)

An argument is usually said to be valid iff it is truth-preserving—iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is normally thought) are not truth-apt. They are not in the business of saying how the world is, and therefore cannot either succeed or fail in doing so. To solve this problem, we need to find a new criterion of validity, and I aim to propose such a criterion.

The purpose of this paper is to explore a new deontic operator for representing what an agent ought to do; the operator is cast against the background of a modal treatment of action developed by Nuel Belnap and Michael Perloff, which itself relies on Arthur Prior's indeterministic tense logic. The analysis developed here of what an agent ought to do is based on a dominance ordering adapted from the decision theoretic study of choice under uncertainty to the present account of (...) action. It is shown that this analysis gives rise to a normal deontic operator, and that the result is superior to an analysis that identifies what an agent ought to do with what it ought to be that the agent does. (shrink)

In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics. We argue that completeness result may be easily regained. Finally, we shortly discuss some issues related to the philosophical intuition behind his approach. This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance (...) Stit Logics. (shrink)

We present a simple theory of actions against the background of branching time, based on which we propose two versions of an extended stit theory, one equipped with particular actions and the other with sets of such actions. After reporting some basic results of a formal development of such a theory, we briefly explore its connection to a version of branching ETL.

One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often not considered explicitly, but rather taken to be a collection of all unclear or troubling cases. However, current philosophy makes a strong point for taking indecision itself to be a proper object of consideration. This paper aims at revealing parallels between (...) the findings concerning indecision in philosophy and the treatment of indecision in argumentation theory. By investigating what philosophical forms and norms of indecision are involved in argumentation theory, we can improve our understanding of the different uncertain evidential situations in argumentation theory. (shrink)

This paper investigates the semantic treatment of conditional obligation, explicit permission (often called positive permission), and prohibition based on models with agents and branched time. In such models branches (rather than moments) are taken as basic, and the branching provides a way to represent the indeterminism which is normally presupposed by talk of free will, responsibility, action and ability. Careful treatment of the relation between ability and responsibility avoids many common problems with accounts of conditional obligation. Recognition of the generality (...) often involved in conditional obligations makes possible a sensitive way of expressing some kinds of general prohibitions, which in turn makes it possible to account for the special role of explicit permission. (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.

We present a theory of actions based on a theory of events in branching time, in which "particular" or "token" actions are taken to be sets of transitions from their initial states to the outcomes. We also present a simple theory of composition of events by which composite events can be formed out of other events. Various kinds of actions, including instantaneous group actions and sequential group actions, are introduced by way of composition, and an extended stit theory of agency (...) is proposed, in which the stit operators are combined or equipped with reified group actions. (shrink)

This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Though there have been productive interactions between moral philosophers and deontic logicians, there has also been a tradition of neglecting the insights that the fields can offer one another. The most sustained interactions between moral philosophers and deontic logicians have notbeen systematic but instead have been scattered across a number of distinct and often unrelated topics. This chapter primarily focuses on three topics. First, we discuss the “actualism/possibilism” debate which, very roughly, concerns the relevance of what one will do at (...) some future time to what one ought to do at present (§2). This topic is also used to introduce various modal deontic logics. Second we discuss the particularism debate which, very roughly, concerns whether there can be any systematic general theory of what we ought to do (§3). This topic is also used to introduce various non-modal deontic logics. Third, we discuss collective action problems which concern the connection between the obligations of individuals and the behavior and obligations of groups of individuals (§4).This topic is also used to discuss formal systems that allow us to study the relationship between individuals and groups. The chapter also contains a general discussion of the relation between ethical theory and deontic logic (§1) and a brief consideration of other miscellaneous topics (§5). (shrink)

Belief revision from the point of view of doxastic logic. Logic Journal of the IGPL, 3(4), 535–553. Segerberg, K. (1995). Conditional action. In G. Crocco, L. Fariñas, & A. Herzig (Eds.), Conditionals: From philosophy to computer science, Studies ...

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...) extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatisation and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the l.. (shrink)

This paper discusses a new aporia, the aporia of future directed beliefs. This aporia contains three propositions: (1) It is possible that there is someone who is infallible that believes something about the future that is not historically settled, (2) it is necessary that someone is infallible if and only if it is necessary that everything she believes is true, and (3) it is necessary that all our beliefs are historically settled. Every claim in this set is intuitively plausible, and (...) there are interesting arguments for or against each of them. Nevertheless, {(1), (2), (3)} entails a contradiction. Consequently, at least one of the sentences in this set must be false. I consider some possible solutions to the problem and discuss some arguments for and against these solutions. Five solutions, in particular, stand out. Three solutions reject (1), one solution rejects (2), and one solution rejects (3). No solution is without problems, and it is not obvious which one we should choose. Yet, we have to give up at least one sentence in {(1), (2), (3)}. This is the nature of an aporia. (shrink)

The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any (...) propositional quantifiers. Then, I will show how these systems can be extended by a couple of propositional quantifiers. I will use a kind of TxW semantics to describe the systems semantically and semantic tableaux to describe them syntactically. Every system will include a constant · that stands for The Good. ‘·’ is read as ‘The Good is realised’. All systems that contain the propositional quantifiers will also include a constant '*' that stands for The Moral Law. '*' is read as ‘The Moral Law is fulfilled’. I will prove that all systems (without the propositional quantifiers) are sound and complete with respect to their semantics and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete. (shrink)

It's natural to think that the principles expressed by the statements "Promises ought to be kept" and "We ought to help those in need" are defeasible. But how are we to make sense of this defeasibility? On one proposal, moral principles have hedges or built-in unless clauses specifying the conditions under which the principle doesn't apply. On another, such principles are contributory and, thus, do not specify which actions ought to be carried out, but only what counts in favor or (...) against them. Drawing on a defeasible logic framework, this paper sets up three models: one model for each proposal, as well as a third model capturing a mixed view on principles that combines them. It then explores the structural connections between the three models and establishes some equivalence results, suggesting that the seemingly different views captured by the models are closer than standardly thought. (shrink)

In this paper, I will discuss some examples of the so-called contrary-to-duty paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us what ought to be the case if something forbidden is true, for example: ‘If she is guilty, she should confess’. Contrary-to-duty obligations are important in our moral and legal thinking. Therefore, we want to be able to find an adequate symbolisation of such obligations in some logical system, a task that has turned out (...) to be difficult. This is shown by the so-called contrary-to-duty paradox. I will investigate and evaluate one kind of solution to this problem that has been suggested in the literature, which I will call the ‘counterfactual solution’. I will use some recent systems that combine not only counterfactual logic and deontic logic, but also temporal logic, in my analysis of the paradox. I will argue that the counterfactual solution has many attractive features and that it can give a fairly satisfactory answer to some examples of the contrary-to-duty paradox, but that it nevertheless has some serious problems. The conclusion is that, notwithstanding the many attractive features of the solution, there seem to be other approaches to the paradox that are more promising. (shrink)

Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon (...) a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language \ of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of \ with respect to other modal languages is a variety of operators having to do with fictional truth, including a ‘fictionality’ operator \ . Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for. (shrink)

I examine an intuitive property of folk-psychological explanations I call self-sufficiency. I argue that individualism cannot honor this property and work toward distilling an account of psychological explanation that does honor it, given some fairly standard assumptions. In doing so, my preference for an Externalist individuation of intentional state will emerge unambiguously. The assumptions I rely on are fairly standard but not uncontroversial. Yet not always do I attempt to defend them from objections. My goal is an account of folk (...) psychology consistent with our every-day practices rather than the deduction of an idealized psychology from first principles. I conclude with some applications offered as evidence that the goal was achieved. (shrink)

The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...) respect to (iii) the presence in T1 of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of T1. (shrink)