Model Transformers for Dynamical Systems of Dynamic Epistemic Logic - LORI-V 2015 (original) (raw)

General dynamic dynamic logic

Advances in Modal Logics, 2012

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the definition of complex modalities. We provide a common generalisation: a logic that is 'dynamic'in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and significantly generalises, all the features of existing extensions of DEL such as BMS [1] and LCC [15]. ...

1995: Reasoning about Action in Dynamic Logic

We study an approach to reasoning about action and change in a dynamic logic setting and provide a solution to problems which are related to tbe frame problem. Unlike most work on the frame problem the logic described in this paper is TTWnotonic and (implicitly) allows for the occurrence of actions of multiple agents. The need to state a large number of "frame axioms" is alleviated by introducing a concept of chronolcgicaJ. pfUervation to dynamic logic. As a side effect, this concept permits to encode temporoi properties in a natural way. We compare the relative merits of our approach and nonmonotonic approaches facing different aspects of the frame problem. It can be shown that the resulting extended systems of propositional dynamic logic preserve (weak) completeness, finite model property and decidability.

Connecting dynamic epistemic and temporal epistemic logics

Logic Journal of IGPL, 2013

We give a relation between a logic of knowledge and change, with a semantics on Kripke models, and a logic of knowledge and time, with a semantics on interpreted systems. In particular, given an epistemic state (pointed Kripke model with equivalence relations) and a formula in a dynamic epistemic logic (a logic describing the consequences of epistemic actions), we construct an interpreted system relative to that epistemic state and that formula that satisfies the translation of the formula into a temporal epistemic logic. The construction involves that the protocol that is implicit in the dynamic epistemic formula, i.e., the set of sequences of actions being executed to evaluate the formula, is made explicit. We first focus on the logic of knowledge and change that is known as public announcement logic, then generalize our results to a dynamic epistemic logic. When compared to Kripke (possible worlds) models, interpreted systems have at least two appealing features: a natural accessibility relation between domain objects, and an equally natural notion of dynamics, modelled by runs. The accessibility relation as we know it from the possible worlds model is in this case grounded; it has a direct and natural interpretation, as follows. In an interpreted system, the role of possible worlds is performed by global states, which are constituted by the agents' local states and the state of the environment. Each agent knows exactly its own local state and the possible local states of other agents: two global states are indistinguishable for an agent if his local compartment is the same. Secondly, an interpreted system defines a number of runs through such global states (i.e., a sequence of global states). Each run corresponds to a possible computation allowed by a protocol. In an object language with temporal and epistemic operators one can then express temporal properties such as liveness and temporal epistemic properties such as perfect recall.

General Dynamic Dynamic Logic (2012)

in Thomas Bolander, Torben Brauner, Silvio Ghilardi, and Lawrence Moss, eds, Advances in Modal Logic, Volume 9, pp.239--260. College Publications, London, 2012.

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the de nition of complex modalities. We provide a common generalisation: a logic that is `dynamic' in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and signi cantly generalises, all the features of existing extensions of DEL such as BMS [3] and LCC [21]. Our dynamic operators work in two steps. First, they provide a multiplicity of transformations of the original model, one for each `action' in a purely syntactic `action structure' (in the style of BMS). Second, they specify how to combine these multiple copies to produce a new model. In each step, we use the generality of PDL to specify the transformations. The main technical contribution of the paper is to provide an axiomatisation of this `general dynamic dynamic logic' (GDDL). This is done by providing a computable translation of GDDL formulas to equivalent PDL formulas, thus reducing the logic to PDL, which is decidable. The proof involves switching between representing programs as terms and as automata. We also show that both BMS and LCC are special cases of GDDL, and that there are interesting applications that require the additional generality of GDDL, namely the modelling of private belief update. More recent extensions and variations of BMS and LCC are also discussed.

Symbolic model checking for Dynamic Epistemic Logic — S5 and beyond*

Journal of Logic and Computation, 2017

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, existing DEL implementations are ad-hoc, so we do not know how the framework really performs. For this purpose, we want to hook up with the best available model-checking and SAT techniques in computational logic. We do this by first providing a bridge: a new faithful representation of DEL models as so-called knowledge structures that allow for symbolic model checking. For more complex epistemic change we introduce knowledge transformers analogous to action models. Next, we show that we can now solve well-known benchmark problems in epistemic scenarios much faster than with existing methods for DEL. We also compare our approach to model checking for temporal logics. Finally, we show that our method is not just a matter of implementation, but that it raises significant issues about logical representation and update. 7

Dynamical Logic Driven by Classified Inferences Including Abduction

2010

We propose a dynamical model of formal logic which realizes a representation of logical inferences, deduction and induction. In addition, it also represents abduction which is classified by Peirce as the third inference following deduction and induction. The three types of inference are represented as transformations of a directed graph. The state of a relation between objects of the model fluctuates between the collective and the distinctive. In addition, the location of the relation in the sequence of the relation influences its state.

A General Dynamic Dynamic Logic

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the definition of complex modalities. We provide a common generalisation: a logic that is `dynamic' in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and significantly generalises, all the features of existing extensions of DEL such as BMS [1] and LCC [2]. Our dynamic operators work in two steps. First, they provide a multiplicity of transformations of the original model, one for each `action' in a purely syntactic `action model' (in the style of BMS). Second, they specific how to combine these multiple copies to produce a new model. In each step, we use the generality of PDL to specify the transformations. The main technical contribution of the paper is to provide an axiomatisation of this `general dynamic dynamic logic' (GDDL). This is done by providing a computable translation of GDDL formulas to equivalent PDL formulas, thus reducing the logic to PDL, which is decidable. The proof involves switching between representing programs as terms and as automata. We also show that both BMS and LCC are special cases of GDDL, and that there are interesting applications that require the additional generality of GDDL, namely the modelling of private belief update. [1] Baltag, A., L. S. Moss and S. Solecki, The logic of public announcements, common knowledge and private suspicious, Technical Report SEN-R9922, CWI, Amsterdam (1999). [2] van Benthem, J., J. van Eijck and B. Kooi, Logics of communication and change, Information and computation 204 (2006), pp. 1620–1662.

Logical Dynamics and Dynamical Systems (PhD Thesis)

Lund University Publications, 2018

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.

An essay in combinatory dynamic logic

Information and Computation, 1991

The theory developed here, although deriving its motivation and parts of its terminology from programming theory, can be viewed as a theory for reasoning about action in general; hence the term dynamic logic. (Hare], 1979) Syntactically, modal logic in general, and dynamic logic in particular, lacks the "static" notion of possible world, or execution state, which is the essence of its semantics. We introduce the states in the syntax, together with a universe-action, connecting each pair of states. and adopt appropriate axioms; we add the adjective "combinatory" for such a revision of the modal logic.