We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reaso... more We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.
Current dynamic epistemic logics for analyzing effects of informational events often become cumbe... more Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events. After a warm-up stage of analyzing logics for public announcements, our main technical results are expressivity and completeness theorems for a much richer logic that we call LCC. This is a dynamic epistemic logic whose static base is propositional dynamic logic (PDL), inter...
Reasoning by cases, valid as it is in classical mathematics, is not that reliable in the moral do... more Reasoning by cases, valid as it is in classical mathematics, is not that reliable in the moral domain. 'If global warming will change our climate, we do not have the obligation to reduce greenhouse gases (since, by assumption, the climate will change anyhow). If global warming will not change our climate, we do not have the obligation to reduce greenhouse
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal lan... more This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers to the literature.
Propositional dynamic logic (PDk) is complete but not compact. Asa consequence, strong completene... more Propositional dynamic logic (PDk) is complete but not compact. Asa consequence, strong completeness (the property FF 1-) does not hold for the standard finitary axiomatisation. In this paper, we present an infinitary proof system of PDk and prove strongcompleteness. The result is extended to epistemic logic with commonknowledge.
We give some semantic results for an epistemic logic incorporating dynamic operators to describe ... more We give some semantic results for an epistemic logic incorporating dynamic operators to describe information changing events. Such events include epistemic changes, where agents become more informed about the non-changing state of the world, and ontic changes, wherein the world changes. The events are executed in information states that are modeled as pointed Kripke models. Our contribution consists of three semantic results. (i) Given two information states, there is an event transforming one into the other. The linguistic correspondent to this is that every consistent formula can be made true in every information state by the execution of an event. (ii) A more technical result is that: every event corresponds to an event in which the postconditions formalizing ontic change are assignments to `true' and `false' only (instead of assignments to arbitrary formulas in the logical language). `Corresponds' means that execution of either event in a given information state results in bisimilar information states. (iii) The third, also technical, result is that every event corresponds to a sequence of events wherein all postconditions are assignments of a single atom only (instead of simultaneous assignments of more than one atom).
There is a growing literature focused on using logical methods to reason about communities of age... more There is a growing literature focused on using logical methods to reason about communities of agents engaged in some form of social interaction. Much of the work builds upon existing logical frameworks developed by philosophers and com-puter scientists incorporating insights ...
Abstract We provide a strongly complete infinitary proof system for hybrid logic. This proof syst... more Abstract We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. Thus completeness proofs are provided for infinitary hybrid versions of non-compact logics like ancestral logic and Segerberg's modal logic with the bounded chain condition. This extends the completeness result for hybrid logics by Blackburn and Tzakova. Keywords: hybrid logic, strong completeness, non-compact logics, infinitary proof rules
We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reaso... more We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.
Current dynamic epistemic logics for analyzing effects of informational events often become cumbe... more Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events. After a warm-up stage of analyzing logics for public announcements, our main technical results are expressivity and completeness theorems for a much richer logic that we call LCC. This is a dynamic epistemic logic whose static base is propositional dynamic logic (PDL), inter...
Reasoning by cases, valid as it is in classical mathematics, is not that reliable in the moral do... more Reasoning by cases, valid as it is in classical mathematics, is not that reliable in the moral domain. 'If global warming will change our climate, we do not have the obligation to reduce greenhouse gases (since, by assumption, the climate will change anyhow). If global warming will not change our climate, we do not have the obligation to reduce greenhouse
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal lan... more This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers to the literature.
Propositional dynamic logic (PDk) is complete but not compact. Asa consequence, strong completene... more Propositional dynamic logic (PDk) is complete but not compact. Asa consequence, strong completeness (the property FF 1-) does not hold for the standard finitary axiomatisation. In this paper, we present an infinitary proof system of PDk and prove strongcompleteness. The result is extended to epistemic logic with commonknowledge.
We give some semantic results for an epistemic logic incorporating dynamic operators to describe ... more We give some semantic results for an epistemic logic incorporating dynamic operators to describe information changing events. Such events include epistemic changes, where agents become more informed about the non-changing state of the world, and ontic changes, wherein the world changes. The events are executed in information states that are modeled as pointed Kripke models. Our contribution consists of three semantic results. (i) Given two information states, there is an event transforming one into the other. The linguistic correspondent to this is that every consistent formula can be made true in every information state by the execution of an event. (ii) A more technical result is that: every event corresponds to an event in which the postconditions formalizing ontic change are assignments to `true' and `false' only (instead of assignments to arbitrary formulas in the logical language). `Corresponds' means that execution of either event in a given information state results in bisimilar information states. (iii) The third, also technical, result is that every event corresponds to a sequence of events wherein all postconditions are assignments of a single atom only (instead of simultaneous assignments of more than one atom).
There is a growing literature focused on using logical methods to reason about communities of age... more There is a growing literature focused on using logical methods to reason about communities of agents engaged in some form of social interaction. Much of the work builds upon existing logical frameworks developed by philosophers and com-puter scientists incorporating insights ...
Abstract We provide a strongly complete infinitary proof system for hybrid logic. This proof syst... more Abstract We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. Thus completeness proofs are provided for infinitary hybrid versions of non-compact logics like ancestral logic and Segerberg's modal logic with the bounded chain condition. This extends the completeness result for hybrid logics by Blackburn and Tzakova. Keywords: hybrid logic, strong completeness, non-compact logics, infinitary proof rules
Uploads