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.

Stit, a sentence form first introduced in Belnap and Perloff (1988), encourages a modal approach to agency. Von Wright, Chisholm, Kenny, and Castañeda have all attempted modal treatments of agency, while Davidson has rejected such treatments. After a brief explanation of the syntax and semantics of stit and a restatement of several of the important claims of the earlier paper, I discuss the virtues of stit against the background of proposals made by these philososphers.

Stit semantics grows out of a modal tradition in the logic of action that concentrates on an operator representing the agency of an individual in seeing to it that some state of affairs holds, rather than on the actions the individual performs in doing so. The purpose of this paper is to enrich stit semantics, and especially epistemic stit semantics, by supplementing the overall framework with an explicit treatment of action types. We show how the introduction of (...) these new action types allows us to define a modal operator capturing an epistemic sense of agency, and how this operator can be used to express an epistemic sense of ability. (shrink)

Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen.Stit-imagination logic models the imagining agent’s deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present paper combines the two logics, thereby modelling imaginative episodes with (...) deliberately chosen initial input. We use a combination ofstit-imagination logic and a content-sensitive variably strict conditional à la Berto, for which we give a Chellas–Segerberg semantics. The proposed semantics has the following advantages over Berto’s: (i) we model thedeliberate choiceof initial input of imaginative episodes (in a multi-agent setting), (ii) we showframe correspondencesfor axiomatic analogues of Berto’s validities, which (iii) allows thepossibility to disregard axiomsthat might be considered not plausible as principles concerning imaginative episodes. We do not take a definite stance on whether theseshouldbe disregarded but give reasons for why one might want to disregard them. Finally, we compare our semantics briefly with recent work, which aims to model voluntary imagination, and argue that our semantics models different aspects. (shrink)

Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascriptions of conflicting but not inconsistent beliefs and (...) desires as being satisfiable. The proposed bdi-stit logic is defined with respect to branching time frames, and it is shown that this logic is a generalization of a bdi logic based on branching time possible worlds frames (but without temporal operators) and dstit logic. The new bdi-stit logic generalizes bdi and dstit logic in the sense that for any model of bdi or dstit logic, there is an equivalent bdi-stit model. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal (...) frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

We extend epistemic stit theory with a modality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_\alpha \varphi $$\end{document}, meant to express that at some moment agent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} had a present-directed intention toward the realization of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}. The semantics is based on the extension of stit frames with special topologies associated to agents. The open sets of the (...) associated topology are interpreted as present-directed intentions, that support whether an agent had an intention of realizing a specific state of affairs when it chose one of its available actions and executed it. As an important application, we use \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_\alpha \varphi $$\end{document} to formalize intentional action and intentional responsibility. We present an axiom system for our logic of intentionality, and prove that it is sound and complete. (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 provide a Kripke semantics for a STIT logic with the "next" operator. As the atemporal group STIT is undecidable and unaxiomatizable, we are interested in strict fragments of atemporal group STIT. First we prove that the satisfiability problem of a formula of the fragment made up of individual coalitions plus the grand coalition is also NEXPTIME-complete. We then generalize this result to a fragment where coalitions are in a given lattice. We also prove that if we (...) restrict the language to nested coalitions the satisfiability problem is NP-complete if the number of agents is fixed and PSPACE-complete if the number of agents is variable. Finally we embed individual STIT with the "next" operator into a fragment of atemporal group STIT. (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.

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)

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)

STIT logic is a family of logics of agency that have received attention in the literature. Despite a variety of developments, most of the existing studies on STIT logic are based on propositional logic. Such propositional STIT logics have computational advantages, but in these logics it seems difficult to distinguish the de re and de dicto readings of sentences about choice independently of models and assignments. To overcome this expressive limitation, this paper presents a cstit-based atemporal first-order (...) STIT logic and its finite domain version as members of a family of term-modal logics possibly with a generalized axiom of independence of agents. The main result is that our proposed Hilbert-style systems for term-modal logics with the alethic modality, equality and non-rigid terms, when they have the (generalized) axiom of independence of agents only if the number of agents is finite, are strongly complete. In particular, the strong completeness of a Hilbert-style system for our first-order STIT logic of finite domain is proved. (shrink)

In this paper we establish equivalence results for the different semantics for the temporal STIT logic T-STIT, that includes temporal operators and the group agency operator for the grand coalition, and we study a semantics for temporal STIT that is based on the concept of interpreted system à la Fagin et al. We discuss the descriptive adequacy of the above semantics in capturing a given gametheoretical scenario where information about the players is included, and we compare them (...) with traditional BT+AC semantics. Also, we discuss the extension of T-STIT with full groups and the corresponding operators, and we discuss the distinction between frames that impose additivity and superadditivity on the choices of arbitrary groups. © 2018 Elsevier B.V., All rights reserved. (shrink)

We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing, 259–279, 2018).

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)

We propose a refinement of STIT logic to make it suitable to model causal agency and responsibility in basic multi-agent scenarios in which agents can interfere with one another. We do this by supplementing STIT semantics, first, with action types and, second, with a relation of opposing between action types. We exploit these novel elements to represent a test for potential causation, based on an intuitive notion of expected result of an action, and two tests for actual causation (...) from the legal literature, i.e. the but-for and the NESS tests. We then introduce three new STIT operators modeling corresponding notions of causal responsibility, which we call potential, strong, and plain responsibility, and use them to provide a fine-grained analysis of a number of case studies involving both individual agents and groups. (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)

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.

In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality , where is any natural number . The basic idea in the proof is to (...) apply the notion of companions to stit sentences in finding busy choice sequences in structures, and to make use of a relation between chains of busy choice sequences and generalized refref conditionals in connecting the two conditions of uncompactness mentioned above. (shrink)

The aim of this paper, is to provide a logical framework for reasoning about actions, agency, and powers of agents and coalitions in game-like multi-agent systems. First we define our basic Dynamic Logic of Agency (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{DLA}}$$\end{document}). Differently from other logics of individual and coalitional capability such as Alternating-time Temporal Logic (ATL) and Coalition Logic, in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{DLA}}$$\end{document} cooperation modalities for expressing powers of agents (...) and coalitions are not primitive, but are defined from more basic dynamic logic operators of action and (historic) necessity. We show that STIT logic can be reconstructed in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{DLA}}$$\end{document}. We then extend \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{DLA}}$$\end{document} with epistemic operators, which allows us to distinguish capability and power. We finally characterize the conditions under which agents are aware of their capabilities and powers. (shrink)

STIT logic is a family of logics of agency that have received attention in the literature. Despite a variety of developments, most of the existing studies on STIT logic are based on propositional logic. Such propositional STIT logics have computational advantages, but in these logics it seems difficult to distinguish the _de re_ and _de dicto_ readings of sentences about choice independently of models and assignments. To overcome this expressive limitation, this paper presents a cstit-based atemporal first-order (...) STIT logic and its finite domain version as members of a family of term-modal logics possibly with a generalized axiom of independence of agents. The main result is that our proposed Hilbert-style systems for term-modal logics with the alethic modality, equality and non-rigid terms, when they have the (generalized) axiom of independence of agents only if the number of agents is finite, are strongly complete. In particular, the strong completeness of a Hilbert-style system for our first-order STIT logic of finite domain is proved. (shrink)

We consider the propositional logic equipped withChellas stitoperators 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)

We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles (...) that relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. (shrink)

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)

A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.

We present in this paper an axiomatization of Belnap and Perloff's stit theory (a logic of "seeing to it that") with a single agent. The idea of the proof is to apply the notion of companion sets--the same notion as used in another paper by the author that showed the decidability of stit theory with a single agent and Refref equivalence.

In the paper, we consider the decision problem of two group achievement stit logics: the super-additive group achievement stit logic and the additive group achievement stit logic, both with refref equivalence. They are the sets of formulas that are valid on two distinct classes of branching time and agent choice structures with instants, respectively. In one class, all structures are super-additive, and in the other class, all structures are additive. Moreover, neither of these structures contains busy choice (...) sequences. We establish the decidability of the super-additive group achievement stit logic with refref equivalence, whereas the additive group achievement stit logic with refref equivalence is shown to be undecidable whenever the number of agents exceeds 2. As additional results, we obtain an alternative but more straightforward semantics for the group achievement stit logics and an embedding of the group Chellas stit logics into the group achievement stit logics with refref equivalence. (shrink)

In this paper, we consider two different ways in which modus-ponens type reasoning with conditional obligations may be formalized. We develop necessary and sufficient conditions for the validity of each, and make some philosophical observations about the differences between the minor premises that each formalization requires. All this is done within the context of the Belnap-Perloff stit theory.

Frankfurt-style examples aim to undermine the principle that moral responsibility requires the ability to do otherwise, which in turn requires the availability of alternate possibilities.1 They are thus considered a reason for refuting incompatibilism. One lesson drawn from Frankfurt-style examples is exemplified by the compatibilist account of Fischer and Ravizza.2 They accept the impact of Frankfurt-style cases and hold that the incompatibilist requirement of regulative control, which involves the agent’s ability to perform the action and her ability to perform the (...) contrary action, must be dropped. In its stead, they propose the weaker requirement of guidance control, which only demands the agent’s causal control over the action for which she is to be held responsible. (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)

We extend stit logic by adding a spatial dimension. This enables us to distinguish between powers and opportunities of agents. Powers are agent-specific and do not depend on an agent’s location. Opportunities do depend on locations, and are the same for every agent. The central idea is to define the real possibility to see to the truth of a condition in space and time as the combination of the power and the opportunity to do so. The focus on agent-relative (...) powers and space-relative opportunities firmly roots effectivity of an autonomous choice making agent in a space–time picture. Our space–time view will be classically Newtonian, since we will assume relativistic phenomena do not play a role in agentive effectivity. We show how our semantics naturally distinguishes between different kinds of histories; histories that reflect real possibilities and histories that reflect counterfactual possibilities. Furthermore, we discuss how the spatial picture sheds light on conceptual problems plaguing the central stit property of ‘independence of agency’. At several points in the article we will emphasise and defend the differences with Belnap’s theory of agency in relativistic branching space–times. (shrink)

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)

We introduce topomatics, a formal framework for the analysis of normative interaction between actors. Each actor is defined by an axiomatic code Ω(A) = ⟨O(A), F(A)⟩: a finite weighted system of obligations and prohibitions interpreted over a finite set of possible worlds. The normative significance ρᴀ(Oᵢ) of each obligation is defined as the total weight of prohibitions logically violated by its non-fulfilment, inducing an endogenous ranking of the code from which the normative core Oᶜᵒʳᵉ(A, θ) and the target world W*(A, (...) θ) are derived at each threshold θ ∈ (0, 1]. We prove four theorems on the normative core: (T1) W*(A, θ) is anti-monotone in θ; (T2) the maximum feasible threshold Θᴀ = sup{θ : W*(A, θ) ≠ ∅} is well-defined and attained; (T3) core coherence is equivalent to the existence of a world satisfying all core formulae simultaneously; (T4) core incoherence implies positive internal tension Sᵢⁿₜ(A) > 0, but not conversely. For two actors A and B we define the feasibility set Φ(A, B) = {(θᴀ, θᴮ) : θᴀ ≤ Θᴀ, θᴮ ≤ Θᴮ, W*(A, θᴀ) ∩ W*(B, θᴮ) ≠ ∅} and establish: (T5) a necessary and sufficient condition for Φ(A, B) ≠ ∅; (T6) a sufficient condition for Φ(A, B) = ∅ via the mirror core configuration; (T7) a threshold asymmetry criterion identifying which actor bears the greater burden of core reduction. Theorem T8 gives the three-way structural classification: mutual feasibility (θ₀, θ₀) ∈ Φ; deferred feasibility Φ ≠ ∅ but (θ₀, θ₀) ∉ Φ; and joint infeasibility Φ = ∅. The framework is related to STIT-logic and input/output logic; its distinguishing feature is that the normative ranking of the code is derived endogenously from the conflict structure rather than imposed externally. (shrink)

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that (...) has been proposed in previous work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL. (shrink)

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 paper aims to construct a logic of alternative-I that provides a proper conceptual framework for talk of possible-I in decision-making context, and thereby solves what we call the paradox of possible-I. The model of our logic, Alt-I model, is an adaptation of N. Belnap’s branching-time model, and the STIT (see to it that) operator defined on the model serves to represent choices and decisions made by actual and counterfactual agents. We conclude this paper by discussing the application of (...) Alt-I model to the case of digital twins, digital copies of a person. (shrink)

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability (...) classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. (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)

Stit theory (a logic of seeing-to-it-that) is applied to cases involving many agents. First treated are complex nestings of stits involving distinct agents. The discussion is driven by the logical impossibility of "a sees to it that b sees to it that Q" in the technical sense, even though that seems to make sense in everyday language, Of special utility are the concepts of "forced choice", of the creation of deontic states, and of probabilities, Second, joint agency, both plain (...) and strict (every participant is essential) is given a rigorous treatment. A central theorem is that strict joint agency is itself agentive. (shrink)