Papers by Rasmus K Rendsvig
Convergence, continuity, recurrence and Turing completeness in dynamic epistemic logic1
Journal of Logic and Computation
The paper analyses dynamic epistemic logic from a topological perspective. The main contribution ... more The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the Stone topology, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behaviour of said maps. Among the recurrence results, we show maps induced by finite action models may have uncountably many recurrent points, even when initiated on a finite input model. Several recurrence results draws on the class of action models being Turing complete, for which the paper provides proof in the pos...
Intensional Protocols for Dynamic Epistemic Logic
Journal of Philosophical Logic
Infostorms
Metaphilosophy, 2013
ABSTRACT It has become a truism that we live in so-called information societies where new informa... more ABSTRACT It has become a truism that we live in so-called information societies where new information technologies have made information abundant. At the same time, information science has made us aware of many phenomena tied to the way we process information. This article explores a series of socio-epistemic information phenomena resulting from processes that track truth imperfectly: pluralistic ignorance, informational cascades, and belief polarization. It then couples these phenomena with the hypothesis that modern information technologies may lead to their amplification so as to give rise to what are called “infostorms.” This points to the need for studying further the exact relations between information technologies and such infostorms, as well as the ways we may design technologies to avoid being misled away from what we have good reasons to believe.
Dynamic Logics for Threshold Models and their Epistemic Extension
Logic, Rationality, and Interaction (LORI 2017), 2017
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution ... more The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.
We take a logical approach to threshold models, used to study the diffusion of opinions, new tech... more We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this adoption policy, threshold models develop dynamically towards a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors' behavior allows agents to anticipate changes in behavior of their closer neighbors. Overall, our logical formalism captures the interplay between the epistemic and social dimensions in social networks.
Model Transformers for Dynamical Systems of Dynamic Epistemic Logic, Oct 1, 2015
This paper takes a dynamical systems perspective on the semantic structures of dynamic epistemic ... more This paper takes a dynamical systems perspective on the semantic structures of dynamic epistemic logic (DEL) and asks the question which orbits DEL-based dynamical systems may produce. The class of dynamical systems based directly on action models produce very limited orbits. Three types of more complex model transformers are equivalent and may produce a large class of orbits, suitable for most modeling purposes.
Proceedings of Epistemic Logic for Individual, Social, and Interactive Epistemology (ELISIEM, ESSLLI 2014), 2014
We take a logical approach to threshold models, used to study the diffusion of e.g. new technolog... more We take a logical approach to threshold models, used to study the diffusion of e.g. new technologies or behaviours in social networks. In short, threshold models consist of a network graph of agents connected by a social relationship and a threshold to adopt a possibly cascading behaviour. Agents adopt new behaviour when the proportion of their neighbours who have already adopted it meets the threshold. Under this adoption policy, threshold models develop dynamically with a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbours' behaviours allows agents to anticipate changes in behaviour of their closer neighbours. It is shown that this epistemic prediction dynamics is equivalent to the non-epistemic threshold model dynamics if and only if agents know exactly their neighbours' behaviour. We further show results regarding fixed points and convergence speed, and provide a partial set of reduction laws, venues for further research, and graphical representations of the dynamics.
The goal of the present paper is to construct a formal explication of the pluralistic ignorance e... more The goal of the present paper is to construct a formal explication of the pluralistic ignorance explanation of the bystander effect. The social dynamics leading to inaction is presented, decomposed, and modeled using dynamic epistemic logic augmented with ‘transition rules’ able to characterize agent behavior. Three agent types are defined: First Responders who intervene given belief of accident; City Dwellers, capturing ‘apathetic urban residents’ and Hesitators, who observe others when in doubt, basing subsequent decision on social proof. It is shown how groups of the latter may end in a state of pluralistic ignorance leading to inaction. Sequential models for each agent type are specified, and their results compared to empirical studies. It is concluded that only the Hesitator model produces reasonable results.
It has become a truism that we live in so-called information societies where new information tech... more It has become a truism that we live in so-called information societies where new information technologies have made information abundant. At the same time, information science has made us aware of many phenomena tied to the way we process information. This article explores a series of socio-epistemic information phenomena resulting from processes that track truth imperfectly: pluralistic ignorance, informational cascades, and belief polarization. It then couples these phenomena with the hypothesis that modern information technologies may lead to their amplification so as to give rise to what are called “infostorms.” This points to the need for studying further the exact relations between information technologies and such infostorms, as well as the ways we may design technologies to avoid being misled away from what we have good reasons to believe.
In the 1992 paper [1] Bikchandani et al. show how it may be rational for Bayesian agents in a seq... more In the 1992 paper [1] Bikchandani et al. show how it may be rational for Bayesian agents in a sequential decision making scenario to ignore their private information and conform to the choices made by previous agents. If this occurs, an agent ignoring her private information is said to be in a cascade.
Dynamics pertaining to learning from the actions of others are modeled with focus on a running ex... more Dynamics pertaining to learning from the actions of others are modeled with focus on a running example, showing how we may come to conclusions regarding an ontic fact solely by observing others act on their beliefs regarding the fact in question. The tools used are elements from dynamic epistemic logic, with the addition of decision and interpretation rules, allowing local, rule-based choice and reasoning about such.
Proceedings of the Logic & Cognition Workshop at ESSLLI 2012
The present paper discusses Frege’s Puzzle about Identity as an argument against a Millian theory... more The present paper discusses Frege’s Puzzle about Identity as an argument against a Millian theory of meaning for proper names. The key notion here is semantic competence. Strict notions of semantic competence are extrapolated from a two-sorted first-order epistemic logical modeling of a cognitive neuropsychological theory of the structure of lexical competence. The model allows for a rigorous analysis of Frege’s argument. The theory and model of lexical semantic competence includes a multitude of types of competence, each yielding a different argument, far from all being as decisive against Millianism as has been the mainstream assumption in 20th century philosophy of language.
Theses by Rasmus K Rendsvig
Lund University Publications, 2018
This thesis is on information dynamics modeled using *dynamic epistemic logic* (DEL). It takes th... more This thesis is on information dynamics modeled using *dynamic epistemic logic* (DEL). It takes the simple perspective of identifying models with maps, which under a suitable topology may be analyzed as *topological dynamical systems*. It is composed of an introduction and six papers. The introduction situates DEL in the field of formal epistemology, exemplifies its use and summarizes the main contributions of the papers.
Paper I models the information dynamics of the *bystander effect* from social psychology. It shows how augmenting the standard machinery of DEL with a decision making framework yields mathematically self-contained models of dynamic processes, a prerequisite for rigid model comparison.
Paper II extrapolates from Paper I's construction, showing how the augmentation and its natural peers may be construed as maps. It argues that under the restriction of dynamics produced by DEL dynamical systems still falls a collection rich enough to be of interest.
Paper III compares the approach of Paper II with *extensional protocols*, the main alternative augmentation to DEL. It concludes that both have benefits, depending on application. In favor of the DEL dynamical systems, it shows that extensional protocols designed to mimic simple, DEL dynamical systems require infinite representations.
Paper IV focuses on *topological dynamical systems*. It argues that the *Stone topology* is a natural topology for investigating logical dynamics as, in it, *logical convergence* coinsides with topological convergence. It investigates the recurrent behavior of the maps of Papers II and III, providing novel insigths on their long-term behavior, thus providing a proof of concept for the approach.
Paper V lays the background for Paper IV, starting from the construction of metrics generalizing the Hamming distance to infinite strings, inducing the Stone topology. It shows that the Stone topology is unique in making logical and topological convergens coinside, making it the natural topology for logical dynamics. It further includes a metric-based proof that the hitherto analyzed maps are continuous with respect to the Stone topology.
Paper VI presents two characterization theorems for the existence of *reduction laws*, a common tool in obtaining complete dynamic logics. In the compact case, continuity in the Stone topology characterizes existence, while a strengthening is required in the non-compact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems.
In the present thesis, a theory of semantic competence is modeled using tools from epistemic logi... more In the present thesis, a theory of semantic competence is modeled using tools from epistemic logic. The resulting formal model is used to analyze a problem from the philosophy of language, namely Frege's Dilemma. There are two aims of the thesis: to construct a formal theory of semantic competence, and to show that the formal theory can be used as an useful analytical tool in uncovering the informational structure behind problems from the philosophy of language. The first aim is achieved by, first, deciding for which theory of meaning a theory of semantic competence is wanted. Due to its simplicity, Millianism is chosen. Then various non-formal theories of semantic competence are evaluated with respect to finding one which allows for an objective, inter-subjective comparison of competence levels. It is argued that the conceptual theory of (Marconi, 1997) is the best choice: the theory has a clearly defined structure making modeling possible, and is based on empirical studies from cognitive neuropsychology. Following these initial choises, the modeling framework and its philosophical interpretation is presented. The framework used is epistemic logic, and both the propositional and quantified versions are introduced. As a more expressible logical language is required, manysorted quantified epistemic logic is presented, and a novel, general completeness result is shown for many-sorted extensions of quantified modal logic. Having thus set the stage of achieving the first aim, a slightly simplified version of the theory of (Marconi, 1997) is modeled. A suitable model-class is defined and a meaning function is added to capture Millian meaning. Based on the shown completeness result, a sound and complete axiom system is presented, and a logic representing the formal theory is thereby found. The model is then validated. It is shown that both the essential ontological properties as well as the competence types from Marconi's theory are present. It is further shown that the formal counterparts of the competence types from Marconi's theory adhere to the principles dictated by empirical studies. Thereby, the first aim is achieved. To accomplish the second aim, proof of concept is shown. This is done by analyzing an objection to the correctness of the Millian theory of meaning, namely Frege's Dilemma (Frege, 1892). The formal theory is used to analyze both disjuncts of the dilemma, while focusing on the epistemic situation of the agent, i.e. the agent's level of semantic competence. The formal theory of semantic competence allows for multiple notions of semantic competence, each resulting in a unique rendering of the dilemma. Based on these analyses, it it is concluded that once the underlying informational structure of the discussed situations is revealed, neither disjunct proves to be a problem for the Millian theory of meaning. Hereby, the second aim is accomplished. However, I raise an intuitive objection to one of the analyses. It is argued that the objection introduces an un-accounted for parameter, namely contexts. In order to show that this objection is not fatal for the proposed analysis, a chapter is devoted to the construction of a contextual theory of semantic competence. The notion of contexts is incorporated into the models for semantic competence, and the possibilities for finding a complete axiomatic system is discussed, but no completeness result is shown. Therefore, a formal theory, i.e. a logic, for contextual semantic competence is not presented. However, the model-theoretic machinery is used to re-analyze the problematic case. It is shown that when the situation is modeled in a contextual model, the epistemic analysis of the disjunct again showed the Puzzle about Identity is unproblematic for the Millian view. Overall, the constructed formal theory of semantic competence is shown to elucidate informational aspects of the problems posed to the philosophy of language by Frege's Dilemma. In particular, once the informational structure of the problems is clear, it is shown that each argument is far from being as decisive against Millianism as has been the mainstream view in 20th century philosophy of language.
Edited Volumes by Rasmus K Rendsvig
Pristine Perspectives on Logic, Language, and Computation
Lecture Notes in Computer Science, 2014
ABSTRACT The articles of this volume will be reviewed individually. For the student sessions of E... more ABSTRACT The articles of this volume will be reviewed individually. For the student sessions of ESSLLI 2010 and ESSLLI 2011 see [Zbl 1250.03008].
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Papers by Rasmus K Rendsvig
Theses by Rasmus K Rendsvig
Paper I models the information dynamics of the *bystander effect* from social psychology. It shows how augmenting the standard machinery of DEL with a decision making framework yields mathematically self-contained models of dynamic processes, a prerequisite for rigid model comparison.
Paper II extrapolates from Paper I's construction, showing how the augmentation and its natural peers may be construed as maps. It argues that under the restriction of dynamics produced by DEL dynamical systems still falls a collection rich enough to be of interest.
Paper III compares the approach of Paper II with *extensional protocols*, the main alternative augmentation to DEL. It concludes that both have benefits, depending on application. In favor of the DEL dynamical systems, it shows that extensional protocols designed to mimic simple, DEL dynamical systems require infinite representations.
Paper IV focuses on *topological dynamical systems*. It argues that the *Stone topology* is a natural topology for investigating logical dynamics as, in it, *logical convergence* coinsides with topological convergence. It investigates the recurrent behavior of the maps of Papers II and III, providing novel insigths on their long-term behavior, thus providing a proof of concept for the approach.
Paper V lays the background for Paper IV, starting from the construction of metrics generalizing the Hamming distance to infinite strings, inducing the Stone topology. It shows that the Stone topology is unique in making logical and topological convergens coinside, making it the natural topology for logical dynamics. It further includes a metric-based proof that the hitherto analyzed maps are continuous with respect to the Stone topology.
Paper VI presents two characterization theorems for the existence of *reduction laws*, a common tool in obtaining complete dynamic logics. In the compact case, continuity in the Stone topology characterizes existence, while a strengthening is required in the non-compact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems.
Edited Volumes by Rasmus K Rendsvig