Online research in philosophy

We present a direct reduction of dynamic epistemic logic in the spirit of [4] to propositional dynamic logic (PDL) [17, 18] by program transformation. The program transformation approach associates with every update action a transformation on PDL programs. These transformations are then employed in reduction axioms for the update actions. It follows that the logic of public announcement, the logic of group announcements, the logic of secret message passing, and so on, can all be viewed as subsystems of PDL. Moreover, the program transformation approach can be used to generate the appropriate reduction axioms for these logics. Our direct reduction of dynamic epistemic logic to PDL was inspired by the reduction of dynamic epistemic logic to automata PDL of [13]. Our approach shows how the detour through automata can be avoided.

We show how belief revision can be treated systematically in the format of dynamic- epistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various ab- stract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.

This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper (J Logic Lang Inform 12(4):381–408, 2003) and to relate these extensions to ones made in van Benthem et al. (Proceedings of LOFT’06. Liverpool, 2006). Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper (van Benthem et al., Proceedings of LOFT’06. Liverpool, 2006) extends (Kooi, J Logic Lang Inform 12(4):381–408, 2003) to using action models, but in both papers, the probabilities are discrete, and are defined on trivial σ -algebras over finite sample spaces. The first extension offered in this paper is to add a previous-time operator to a probabilistic dynamic epistemic logic similar to Kooi’s in (J Logic Lang Inform 12(4):381–408, 2003). The other is to involve non-trivial σ -algebras and continuous probabilities in probabilistic dynamic epistemic logic.

This paper introduces DEMO, a Dynamic Epistemic Modelling tool. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula evaluation in epistemic models, translation of dynamic epistemic formulas to PDL formulas, and so on. The paper implements the reduction of dynamic epistemic logic [16, 2, 3, 1] to PDL given in [12]. The reduction of dynamic epistemic logic to automata PDL from [24] is also discussed and implemented. Epistemic models are minimized under bisimulation, and update action models are minimized under action emulation (the appropriate structural notion for having the same update effect, cf. [13]). The paper is an exemplar of tool building for epistemic update logic. It contains the full code of an implementation in Haskell [22], in ‘literate programming’ style [23], of DEMO.

Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents, based on semantic information. The latter is produced by acts of observation or communication, that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference – and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we extend earlier epistemic “awareness models” into a dynamic system that includes acts of public observation, but also adding and dropping formulas from the currently ‘entertained’ set, we give a completeness theorem, and we show how this dynamics updates explicit knowledge. Similar ideas have been proposed before, but they were restricted to update with factual propositions; our new dynamic system applies to arbitrary formulas. We also extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches.

Formal learning theory constitutes an attempt to describe and explain the phenomenon of learning, in particular of language acquisition. The considerations in this domain are also applicable in philosophy of science, where it can be interpreted as a description of the process of scientific inquiry. The theory focuses on various properties of the process of hypothesis change over time. Treating conjectures as informational states, we link the process of conjecture-change to epistemic update. We reconstruct and analyze the temporal aspect of learning in the context of dynamic and temporal logics of epistemic change. We first introduce the basic formal notions of learning theory and basic epistemic logic. We provide a translation of the components of learning scenarios into the domain of epistemic logic. Then, we propose a characterization of finite identifiability in an epistemic temporal language. In the end we discuss consequences and possible extensions of our work.

Logical frameworks for analysing the dynamics ofinformation processing abound [4, 5, 8, 10, 12, 14, 20, 22]. Some of these frameworks focus on the dynamics of the interpretation process, some on the dynamics of the process of drawing inferences, and some do both of these. Formalisms galore, so it is felt that some conceptual streamlining would pay off. This paper is part of a larger scale enterprise to pursue the obvious parallel between information processing and imperative programming. We demonstrate that logical tools from theoretical computer science are relevant for the logic of information flow. More specifically, we show that the perspective of bare logic [13, 18] can fruitfully be applied to the conceptual simplification of information flow logics. Part one of this program consisted of the analysis of 'dynamic interpretation' in this way, using the example of dynamic predicate logic [10]; the results were published in [7]. The present paper constitutes the second part of the program, the analysis of 'dynamic inference'. Here we focus on Veltman’s update logic [22]. Update logic is an example of a logical framework which takes the dynamics of drawing inferences into account by modelling information growth as discarding of possibilities. This paper shows how information logics like update logic can fruitfully be studied by linking their dynamic principles to static 'correctness descriptions'. Our theme is exemplified by providing a sound and complete HoarelPratt style deduction system for update logic. The Hoare/Pratt correctness statements use modal propositional dynamic logic as assertion language and connect update logic to the modal propositional logic S5. The connection with S5 provides a clear link between the dynamic and the static semantics of update logic. The fact that update logic is decidable was noted already in [2]; the connection with S5 provides an alternative proof. The S5 connection can also be used for rephrasing the validity notions of update logic and for performing consistency checks. In conclusion, it is argued that interpreting the dynamic statements of information logics as dynamic modal operators has much wider applicability. In fact, the method can be used to axiomatize quite a wide range of information logics.

This paper shows how propositional dynamic logic (PDL) can be interpreted as a logic for multi-agent belief revision. For that we revise and extend the logic of communication and change (LCC) of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to an update mechanism that handles belief change as relation substitution, and we show that the update part of this logic is more expressive than either that of LCC or that of doxastic/epistemic PDL with a belief change modality. It is shown that the properties of knowledge and belief are preserved under any update, and that the logic is complete.

This talk shows how propositional dynamic logic (PDL) can be interpreted as a logic for multi-agent knowledge update and belief revision, or as a logic of preference change, if the basic relations are read as preferences instead of plausibilities. Our point of departure is the logic of communication and change (LCC) of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to an update mechanism that handles belief change as relation substitution, and we show that the update part of this logic is more expressive than either that of LCC or that of epistemic/doxastic PDL with a belief change modality. Next, we show that the properties of knowledge and belief are preserved under any update, unlike in LCC. We prove completeness of the logic and give examples of its use. If there is time, we will also look at the preference interpretation of the system, and at preference change scenarios that can be modelled with it.

Dynamic update of information states is a new paradigm in logicalsemantics. But such updates are also a traditional hallmark ofprobabilistic reasoning. This note brings the two perspectives togetherin an update mechanism for probabilities which modifies state spaces.