This paper studies intentional action in stit logic. The formal logic study of intentional action appears to be new, since most logical studies of intention concern intention as a static mental state. In the formalization we distinguish three modes of acting: the objective level concerning the choices an agent objectively exercises, the subjective level concerning the choices an agent knows or believes to be exercising, and finally, the intentional level concerning the choices an agent intentionally exercises. Several axioms constraining the (...) relations between these different modes of acting will be considered and discussed. The side effect problem will be analyzed as an interaction between knowingly doing and intentionally doing. Non-successful action will be analyzed as a weakening of the epistemic attitude towards action. Finally, the notion of ‘attempt’ will be briefly considered as a further weakening in this direction. (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)

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we (...) show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

This paper presents two general results of decidability concerning logics based on an indeterministic metric tense logic, which can be applied to, among others, logics combining knowledge, time and agency. We provide a general Kripke semantics based on a variation of the notion of synchronized Ockhamist frames. Our proof of the decidability is by way of the finite frame property, applying subframe transformations and a variant of the filtration technique.

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.

One of the best known approaches to the logic of agency are the ‘stit’ logics. Often, it is not the actions of an individual agent that bring about a certain outcome but the joint actions of a set of agents, collectively. Collective agency has received comparatively little attention in ‘stit’. The paper maps out several different forms, several different senses in which a particular set of agents, collectively, can be said to bring about a certain outcome, and examines how these (...) forms can be expressed in ‘stit’ and stit-like logics. The outcome that is brought about may be unintentional, and perhaps even accidental; the account deliberately ignores aspects such as joint intention, communication between agents, awareness of other agents’ intentions and capabilities, even the awareness of another agent’s existence. The aim is to investigate what can be said about collective agency when all such considerations are ignored, besides mere consequences of joint actions. The account will be related to the ‘strictly stit’ of Belnap and Perloff, 25–48 1993) and their suggestions concerning ‘inessential members’ and ‘mere bystanders’. We will adjust some of those conjectures and distinguish further between ‘potentially contributing bystanders’ and ‘impotent bystanders’. (shrink)

This paper presents proofs of completeness and decidability of a non-temporal fragment of an Xstit logic. This shows a distinction between the non-temporal fragments of Xstit logic and regular stit logic since the latter is undecidable. The proof of decidability is via the finite model property. The finite model property is shown to hold by constructing a filtration. However, the set that is used to filter the models isn’t simply closed under subformulas, it has more complex closure conditions. The filtration (...) set is akin to the Fischer–Ladner closure of a set used to show completeness and decidability of propositional dynamic logic. (shrink)

This article proposes the use of temporal logic for an analysis of instrumentality inspired by the work of G.H. von Wright. The first part of the article contains the philosophical foundations. We discuss von Wright’s general theory of agency and his account of instrumentality. Moreover, we propose several refinements to this framework via rigorous definitions of the core notions involved. In the second part, we develop a logical system called Temporal Logic of Action and Expectations (TLAE). The logic is inspired (...) by a fragment of propositional dynamic logic based on indeterministic time. The system is proven to be weakly complete relative to its given semantics. We then employ TLAE to formalise and analyse the instrumentality relations defined in the first part of the paper. Last, we point out philosophical implications and possible extensions of our work. (shrink)

We consider the propositional logic equipped with Chellas stit operators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does (...) not exceed three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic. (shrink)

In this paper we propose a method for modeling social influence within the STIT approach to action. Our proposal consists in extending the STIT language with special operators that allow us to represent the consequences of an agent’s choices over the rational choices of another agent.

This paper explores the analysis of ability, where ability is to be understood in the epistemic sense—in contrast to what might be called a causal sense. There are plenty of cases where an agent is able to perform an action that guarantees a given result even though she does not know which of her actions guarantees that result. Such an agent possesses the causal ability but lacks the epistemic ability. The standard analysis of such epistemic abilities relies on the notion (...) of action types—as opposed to action tokens—and then posits that an agent has the epistemic ability to do something if and only if there is an action type available to her that she knows guarantees it. We show that these action types are not needed: we present a formalism without action types that can simulate analyzes of epistemic ability that rely on action types. Our formalism is a standard epistemic extension of the theory of “seeing to it that”, which arose from a modal tradition in the logic of action. (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 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)

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of (...) the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings. (shrink)