Proof-Theoretic Analysis of the Logics of Agency: The Deliberative STIT

Negri, Sara; Pavlović, Edi

doi:10.1007/s11225-020-09914-1

Cited by 5 publications

(12 citation statements)

References 17 publications

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“…It is the purpose of this article to demonstrate that these alternative axioms are likewise readily derivable in the system of Negri and Pavlović (2020). As such, in the proceeding we will lean heavily on the results present therein.…”

Section: Introductionmentioning

confidence: 87%

“…Here we are dealing with three systems-axiomatic ones of Belnap et al (2001); Xu (1998) and a sequent calculus from Negri and Pavlović (2020). Given that all three are sound and complete with respect to the background semantics, one should prima facie expect the results of this paper to hold.…”

Section: Introductionmentioning

confidence: 98%

“…The treatment of stit modalities in terms of proof theory remains relatively scant, notable exceptions being (Wansing 2006(Wansing , 2017Wansing 2018, 2019), which all involve a tableaux approach. Approaches utilizing a sequent calculus have been developed recently, in particular (using a simplification of a tableux) van Berkel and ; Lyon and van Berkel (2019) and Negri and Pavlović (2020) (which builds the calculus based on the semantics from Belnap et al 2001). The system from the latter will be used in this paper, since in addition to the usual range of desirable proof-theoretic properties (like the admissibility of contraction and cut), it also offers a structural proof of multi-agent decidability and, even though it focuses on dstit, provides a uniform basis for the treatment of multiple stit modalities.…”

Section: Introductionmentioning

confidence: 99%

“…In order to avoid repeating large swathes of that paper we will not present its proofs, but for ease of reference the results relevant for this paper will be noted in the following section. Throughout the paper we will mark any propositions, theorems or lemmas from Negri and Pavlović (2020) with an asterisk.…”

Section: Introductionmentioning

confidence: 99%

“…However, there is a conceptual priority of an existence of proof to metatheoretical resultsa system is complete because certain proofs exist (the other way around would be putting the cart before the horse), and it is standard practice in proof theory to prefer a direct proof to a roundabout one. Case in point-in Negri and Pavlović (2020) it would not be, strictly speaking, necessary to demonstrate completeness via a failed proof search after already showing that the axioms of Belnap et al (2001) are derivable. However, the former approach, in addition to being elegant, provides the correct conceptual connection between the system and its underlying semantics.…”

Section: Introductionmentioning

confidence: 99%

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Alternative Axiomatization for Logics of Agency in a G3 Calculus

Negri

Pavlović

2021

Found Sci

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In a recent paper, Negri and Pavlović (Studia Logica 1–35, 2020) have formulated a decidable sequent calculus for the logic of agency, specifically for a deliberative see-to-it-that modality, or dstit. In that paper the adequacy of the system is demonstrated by showing the derivability of the axiomatization of dstit from Belnap et al. (Facing the future: agents and choices in our indeterminist world. Oxford University Press, Oxford, 2001). And while the influence of the latter book on the study of logics of agency cannot be overstated, we note that this is not the only axiomatization of that modality available. In fact, an earlier (and arguably purer) one was offered in Xu (J Philosophical Logic 27(5):505–552, 1998). In this article we fill this lacuna by proving that this alternative axiomatization is likewise readily derivable in the system of Negri and Pavlović (Studia Logica 1–35, 2020).

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Alternative Axiomatization for Logics of Agency in a G3 Calculus

Negri

Pavlović

2021

Found Sci

Self Cite

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Mechanising Gödel–Löb Provability Logic in HOL Light

Maggesi,

Perini Brogi

2023

J Autom Reasoning

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We introduce our implementation in HOL Light of the metatheory for Gödel–Löb provability logic (GL), covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself. The strategy we develop here to formalise the modal completeness proof overcomes the technical difficulty due to the non-compactness of GL and is an adaptation—according to the formal language and tools at hand—of the proof given in George Boolos’ 1995 monograph. Our theorem prover for GL relies then on this formalisation, is implemented as a tactic of HOL Light that mimics the proof search in the labelled sequent calculus $$\textsf{G3KGL}$$ G 3 KGL , and works as a decision algorithm for the provability logic: if the algorithm positively terminates, the tactic succeeds in producing a HOL Light theorem stating that the input formula is a theorem of GL; if the algorithm negatively terminates, the tactic extracts a model falsifying the input formula. We discuss our code for the formal proof of modal completeness and the design of our proof search algorithm. Furthermore, we propose some examples of the latter’s interactive and automated use.

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Stit-LOGIC FOR IMAGINATION EPISODES WITH VOLUNTARY INPUT

Badura¹,

Wansing²

2021

The Review of Symbolic Logic

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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 of stit-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 the deliberate choice of initial input of imaginative episodes (in a multi-agent setting), (ii) we show frame correspondences for axiomatic analogues of Berto’s validities, which (iii) allows the possibility to disregard axioms that might be considered not plausible as principles concerning imaginative episodes. We do not take a definite stance on whether these should be 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.

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Proof-Theoretic Analysis of the Logics of Agency: The Deliberative STIT

Cited by 5 publications

References 17 publications

Alternative Axiomatization for Logics of Agency in a G3 Calculus

Alternative Axiomatization for Logics of Agency in a G3 Calculus

Mechanising Gödel–Löb Provability Logic in HOL Light

Stit-LOGIC FOR IMAGINATION EPISODES WITH VOLUNTARY INPUT

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