Epistemic Logic Research Articles

Compromise and Consensus: Toward a Two-Track Model of Deliberation

In this article, we discuss the relationship between deliberative democracy, compromise, and consensus. According to one view, deliberation should aim exclusively at compromise (compromise-only view). According to another view, compromise processes are incompatible with with the epistemic logic of deliberation (no-compromise view). Against the compromise-only view, we argue that it relies on a misunderstanding of the role of consensus and fails to capture how consensus-oriented deliberations are conducive to important learning processes. Against the no-compromise view, we argue that it mistakenly envisages deliberation in purely epistemic terms and that this misunderstands the point and purpose of deliberative democracy as a practical political ideal. By adopting a distinct second-order perspective, we demonstrate how compromise processes can be rendered compatible with a deliberative orientation to finding the best political outcomes. Based on these discussions, we articulate a two-track model of deliberation that shows how deliberative democracy can be dually committed to compromise and consensus.

Synergistic knowledge

Simplicial complexes are a successful model for distributed computing. They have recently been observed to provide an interesting model for epistemic multi-agent logic where the agents' local states are the main building blocks (instead of the global states). A natural generalization is to study epistemic logic on semi-simplicial sets. However, finding the appropriate modal logic for semi-simplicial models has been an open question. We answer this by introducing the logic of synergistic knowledge and establishing its soundness and completeness.

Wanted dead or alive: epistemic logic for impure simplicial complexes

Abstract We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent synchronous distributed systems under uncertainty over which processes are still active (are alive) and which processes have failed or crashed (are dead). Our work generalizes the logic of knowledge for pure simplicial complexes, where all processes are alive, by Goubault et al. In our semantics, given a designated face in a complex, a formula can only be true or false there if it is defined. The following are undefined: dead processes cannot know or be ignorant of any proposition, and live processes cannot know or be ignorant of factual propositions involving processes they know to be dead. The semantics are therefore three-valued, with undefined as the third value. We propose an axiomatization that is a version of the modal logic S5. We also show that impure simplicial complexes correspond to certain Kripke models where agents’ accessibility relations are equivalence relations on a subset of the domain only.

Formalized soundness and completeness of epistemic and public announcement logic

Abstract I strengthen the foundations of epistemic logic by formalizing the family of normal modal logics in the proof assistant Isabelle/HOL. I define an abstract canonical model over any set of axioms and formalize completeness-via-canonicity: when the canonical model for the chosen axioms belongs to a certain class of frames, strong completeness over that class follows immediately. I instantiate the result with logics based on various epistemic principles to obtain completeness results for systems from K to S5. I then move to a family of public announcement logics (PAL) and prove abstract results for strong soundness and completeness. I lift the completeness results from epistemic logic to the setting with public announcements in a modular way. This work formulates the completeness-via-canonicity technique as a proper theorem and demonstrates its applicability. Additionally, it succinctly formalizes the requirements for lifting completeness from bare epistemic logic to the addition of public announcements.

Simplicial models for the epistemic logic of faulty agents

In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher dimensional structures called simplicial complexes. In the original formulation of Goubault et al. (Inf Comput 278:104597, 2021. https://doi.org/10.1016/j.ic.2020.104597), simplicial models are always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf {S5_n}$$\\end{document} semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers (van Ditmarsch, WoLLIC 2021, pp 31–46, 2021. https://doi.org/10.1007/978-3-030-88853-4_3; Goubault et al. STACS 2022, pp 33:1–33:20, 2022. https://doi.org/10.4230/LIPIcs.STACS.2022.33; Goubault et al. LICS, pp 1–13, 2023. https://doi.org/10.1109/LICS56636.2023.10175737), with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.

Inferential knowledge and epistemic dimensions

Abstract Knowledge representation is one way to exploit expertise in a given domain by logical means. But, what kind of knowledge does one acquire from an inference (or inference on a query result over a knowledge base)? Such a question may appear awkward since the answer seems so obvious: from an inference, one simply acquires knowledge. This is undoubtedly the case when only one type of knowledge (for instance, expert knowledge) is involved in an inference. What if several types of knowledge are involved? What type of knowledge can one deduce from a plurality of knowledge types? I claim that reasoning with different knowledge concepts requires a fine-grained representation of knowledge in which every knowledge type finds a singular expression in order to avoid some epistemic equivocity associated with a coarse-grained representation of knowledge. In the first part of the paper, I revisit the Muddy Children Puzzle, which usually serves to illustrate common knowledge in dynamic epistemic logic. I try to show that this problem also shows some sort of epistemic equivocity between concepts of knowledge and, consequently, that the problem calls for some epistemological refinements concerning the representation of the types of knowledge at play in an inference. In the second part, I address this issue from a semantic point of view, and I develop a fragment of epistemic logic capable of providing a solution to the problem of epistemic equivocity.

Topic-Based Communication Between Agents

AbstractCommunication within groups of agents has been lately the focus of research in dynamic epistemic logic. This paper studies a recently introduced form of partial (more precisely, topic-based) communication. This type of communication allows for modelling scenarios of multi-agent collaboration and negotiation, and it is particularly well-suited for situations in which sharing all information is not feasible/advisable. The paper can be divided into two parts. In the first part, we present results on invariance and complexity of model checking. Moreover, we compare partial communication with the public announcement and arrow update settings in terms of both language-expressivity and update-expressivity. Regarding the former, the three settings are equivalent, their languages being equally expressive. Regarding the latter, all three modes of communication are incomparable in terms of update-expressivity. In the second part, we shift our attention to strategic topic-based communication. We do so by extending the language with a modality that quantifies over the topics the agents can ‘talk about’, thus allowing a form of arbitrary partial communication. For this new framework, we provide a complete axiomatisation, showing also that the new language’s model checking problem is PSPACE-complete. Finally, we argue that, in terms of expressivity, this new language of arbitrary partial communication is incomparable to that of arbitrary public announcements and also to that of arbitrary arrow updates.

Epistemic logic with partial grasp

We have to gain from recognizing a relation between epistemic agents and the parts of subject matters that play a role in their cognitive lives. I call this relation “grasping”. Namely, I zone in on one notion of having a partial grasp of a subject matter—that of agents grasping part of the subject matter that they are attending to—and characterize it. I propose that giving up the idealization that we fully grasp the subject matters we attend to allows one to more realistically characterize the epistemic life of agents. To show this, I propose an epistemic logic with partial grasp that has in mind considerations from first-order aboutness theory with the aim of avoiding certain forms of logical omniscience, and which provides an alternative to immanent closure (Yablo Aboutness, Princeton University Press, 2014).

Epistemic Logics for Relevant Reasoners

We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem.

Evoked questions and inquiring attitudes

Abstract Drawing inspiration from the notion of evocation employed in inferential erotetic logic, we defend an ‘evoked questions norm’ on inquiring attitudes. According to this norm, it is rational to have an inquiring attitude concerning a question only if that question is evoked by your background information. We offer two arguments for this norm. First, we develop an argument from convergence. Insights from several independent literatures (20th-century ordinary-language philosophy, inferential erotetic logic, inquisitive epistemic logic, and contemporary zetetic epistemology), all converge on the evoked questions norm. Second, we show that suitably interpreted, the evoked questions norm correctly predicts several underappreciated kinds of bad questions. It does this, in part, by recovering versions of previously defended ignorance and knowledge norms. Some of those bad questions cannot be predicted by either norm singly, but only when corporately taken to reflect a common normative category. We identify this category as evocation.

Modal Knowledge for Expressivists

What does ‘Smith knows that it might be raining’ mean? Expressivism here faces a challenge, as its basic forms entail a pernicious type of transparency, according to which ‘Smith knows that it might be raining’ is equivalent to ‘it is consistent with everything that Smith knows that it is raining’ or ‘Smith doesn’t know that it isn’t raining’. Pernicious transparency has direct counterexamples and undermines vanilla principles of epistemic logic, such as that knowledge entails true belief and that something can be true without one knowing it might be. I re-frame the challenge in precise terms and propose a novel expressivist formal semantics that meets it by exploiting (i) the topic-sensitivity and fragmentation of knowledge and belief states and (ii) the apparent context-sensitivity of epistemic modality. The resulting form of assertibility semantics advances the state of the art for state-based bilateral semantics by combining attitude reports with context-sensitive modal claims, while evading various objectionable features. In appendices, I compare the proposed system to Beddor and Goldstein’s ‘safety semantics’ and discuss its analysis of a modal Gettier case due to Moss.

A Truthmaker-based Epistemic Logic

The aim of this work is to investigate the problem of Logical Omniscience in epistemic logic by means of truthmaker semantics. We will present a semantic framework based on W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{W}$$\\end{document}-models extended with a partial function, which selects the body of knowledge of the agents, namely the set of verifiers of the agent’s total knowledge. The semantic clause for knowledge follows the intuition that an agent knows some information ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\phi }$$\\end{document}, when the propositional content that ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\phi }$$\\end{document} is contained in her total knowledge. We will argue that this idea mirrors the philosophical conception of immanent closure by Yablo (2014), giving to our proposal a strong philosophical motivation. We will discuss the philosophical implications of the semantics and we will introduce its axiomatization.

A possible worlds semantics for trustworthy non-deterministic computations

The notion of trustworthiness, central to many fields of human inquiry, has recently attracted the attention of various researchers in logic, computer science, and artificial intelligence (AI). Both conceptual and formal approaches for modeling trustworthiness as a (desirable) property of AI systems are emerging in the literature. To develop logics fit for this aim means to analyze both the non-deterministic aspect of AI systems and to offer a formalization of the intended meaning of their trustworthiness. In this work we take a semantic perspective on representing such processes, and provide a measure on possible worlds for evaluating them as trustworthy. In particular, we intend trustworthiness as the correspondence within acceptable limits between a model in which the theoretical probability of a process to produce a given output is expressed and a model in which the frequency of showing such output as established during a relevant number of tests is measured. From a technical perspective, we show that our semantics characterizes the probabilistic typed natural deduction calculus introduced in D'Asaro and Primiero (2021)[12] and further extended in D'Asaro et al. (2023) [13]. This contribution connects those results on trustworthy probabilistic processes with the mainstream method in modal logic, thereby facilitating the understanding of this field of research for a larger audience of logicians, as well as setting the stage for an epistemic logic appropriate to the task.

Stalnaker's Epistemic Logic in Isabelle/HOL

Stalnaker's Epistemic Logic in Isabelle/HOL

Logic Meets Wigner’s Friend (and their Friends)

We take a fresh look at Wigner’s Friend thought-experiment and some of its more recent variants and extensions, such as the Frauchiger-Renner (FR) Paradox. We discuss various solutions proposed in the literature, focusing on a few questions: What is the correct epistemic interpretation of the multiplicity of state assignments in these scenarios? Under which conditions can one include classical observers into the quantum state descriptions, in a way that is still compatible with traditional Quantum Mechanics? Under which conditions can one system be admitted as an additional ‘observer’ from the perspective of another background observer? When can the standard axioms of multi-agent Epistemic Logic (that allow “knowledge transfer” between agents) be applied to quantum-physical observers? In the last part of the paper, we propose a new answer to these questions, sketch a particular formal implementation of this answer, and apply it to obtain a principled solution to Wigner Friend-type paradoxes.

Probabilistic epistemic logic based on neighborhood semantics

Probabilistic epistemic logic based on neighborhood semantics

Hyperintensionality and overfitting

A hyperintensional epistemic logic would take the contents which can be known or believed as more fine-grained than sets of possible worlds. I consider one objection to the idea: Williamson’s Objection from Overfitting. I propose a hyperintensional account of propositions as sets of worlds enriched with topics: what those propositions, and so the attitudes having them as contents, are about. I show that the account captures the conditions under which sentences express the same content; that it can be pervasively applied in formal and mainstream epistemology; and that it is left unscathed by the objection.

Addressing Knowledge Gaps in ITSM Practice with “Learning Digital Commons”: A Case Study

AbstractInformation Technology Service Management (ITSM) constitutes a suite of specialized organizational capabilities aimed at optimizing the value derived from IT services. The practice of ITSM encompasses a range of complementary frameworks. However, the practitioner community lacks a comprehensive, holistic understanding of the knowledge embedded within these frameworks.Addressing this gap, we developed Service-Symphony, an instance of a Learning Digital Commons (LEDICO) designed to empower the ITSM community with a holistic knowledge-learning experience, with design principles based on epistemic logic, cognitive constructivist learning theory and cognitive schema theory. Leveraging the Design Science Research (DSR) paradigm, we systematically constructed and assessed Service-Symphony. Evaluation tools included surveys and web analytics. Survey responses revealed a consensus among participants, with the majority expressing alignment with the four design principles underpinning Service-Symphony. Web analytics data further indicated significant engagement, with 148,796 users accessing Service-Symphony between April 2019 and September 2022.This paper contributes both to theory and practice. Theoretical contributions include the establishment of a conceptual model and a multi-grounded design theory based on cognitive constructivist learning, cognitive schema and epistemic logic. The practical contributions include e the deployment of a public domain ITSM digital commons tailored to the specific needs of the ITSM community, which is also used as supplementary learning resource for ITSM students.

Pattern Models: A Dynamic Epistemic Logic For Distributed Systems

Abstract We introduce pattern models, a dynamic epistemic logic for analyzing distributed systems. First, we present a version of pattern models where the full-information protocol, widely studied in distributed computability, is static in the product definition of pattern models. Next, we parametrize such a logic so as to add the capability to model dynamics of arbitrary deterministic protocols. We thus give a systematic construction of pattern models for a large variety of distributed-computing models called dynamic-network models. Using pattern models, the epistemic dynamics of a proper subclass of dynamic-network models called oblivious can be described using a static pattern model, hence using constant space. For this case, we present a sufficient unsolvability condition for the consensus task that can be easily verified analyzing the structure of the initial epistemic model and the pattern model for a given oblivious dynamic-network model.

The KK Principle and the Strong Notion of Knowledge: Hintikka’s Arguments for KK Revisited

In his Knowledge and Belief (1962), Hintikka establishes his system of epistemic logic with the KK (Knowing that One Knows, in symbols, Kp→KKp) principle (KK for short). However, his system of epistemic logic and the KK principle are grounded upon his strong notion of knowledge, which requires that knowledge is infallible, that is, it makes further inquiry pointless, and becomes ‘discussion-stopper’; knowledge implies truth, to wit, cognitive agents will not be mistaken in their knowledge; cognitive agents will be ‘perfect logicians’, i.e. they have infinitive capability of logical inference. Hintikka calls the argument for KK from the strong notion of knowledge as the ‘transcendental argument’ for KK. Obviously, the strong notion of knowledge is far away from our ordinary conception of knowledge; based on such a strong sense of knowledge, epistemic logic has met the problem of logical omnipotence, and is difficult to apply in our ordinary cognitive practice. Moreover, there is no close connection of the KK principle with internalism or externalism.