The gamut of dynamic logics

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.

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.

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.

Journal of Logic Language and Information

Reasoning about change is a central issue in research on human and robot planning. 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 the frame problem. Unlike most work on the flame problem the logic described in this paper is monotonic. It (implicitly) allows for the occurrence of actions of multiple agents by introducing non-stationary notions of waiting and test. The need to state a large number of "frame axioms" is alleviated by introducing a concept of chronological preservation to dynamic logic. As a side effect, this concept permits the encoding of temporal properties in a natural way. We compare the relative merits of our approach and non-monotonic approaches as regards different aspects of the frame problem. Technically, we show that the resulting extended systems of propositional dynamic logic preserve (weak) completeness, finite model property and decidability.

The marriage of logic and objects is a very wide-ranging problem, approached with various approaches, depending on the purpose. In this article, we are interested in the modelling of the state and the change of the state of an object in logic programming. After a state of the art on the subject, presenting the various aspects as well as different solutions proposed in the literature, the article then proposes a mechanism of versions of objects based on the mechanism of unification and on the use incomplete structures. Indeed, the overview of an incomplete structure can be used to allow the entry of new information by means of unification and thus to foresee the future. This mechanism makes it possible to construct the history of an object by unification and to undo it by backtracking. The changes of state are thus made and defeated, without effects of edge, in synchronization with the backtrack.

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

This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about actions. Propositional Dynamic Logics (PDL's) are modal logics for describing and reasoning about system dynamics in terms of properties of states and actions 1 modeled as relations between states (see (Kozen Tiuryn 1990; Harel 1984; Parikh 1981) for surveys on PDL's, see also (Stifling 1992) for a somewhat different account).

2004

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle-the refined extension principle-which is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though based on stable models, complies with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle. This work was partially supported by FEDER financed project FLUX (POSI/40958/SRI/2001) and by project SOCS (IST-2001-32530). Special thanks are due to Pascal Hitzler and Reinhard Kahle for helpful discussions.

Journal of Logic and Computation, 2022

Humans can make a plan by refining abstract actions. Dynamic logic, which enables reasoning about the dynamics of actions, does not support this form of planning. This paper investigates the extension of dynamic logic with a refinement relation that specifies how an abstract action can be refined into a more specific (composite) action. The paper investigates the properties of the refinement relation, the derivation of the refinement relation and a proof system based on a prefixed-tableau.

Lecture Notes in Computer Science, 2003

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle -the refined extension principle -which is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though based on stable models, complies with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.