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AGM Belief Revision in Monotone Modal Logics
"... Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. This paper defines AGM revision operators on several firstorder monotonic modal correspondents, where each firstorder correspondence ..."
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Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. This paper defines AGM revision operators on several firstorder monotonic modal correspondents, where each firstorder correspondence language is defined by Marc Pauly’s version of the van Benthem characterization theorem for monotone modal logic. A revision problem expressed in a monotone modal system is translated into firstorder logic, the revision is performed, and the new belief set is translated back to the original modal system. An example is provided for the logic of Risky Knowledge that uses modal AGM contraction to construct counterfactual evidence sets in order to investigate robustness of a probability assignment given some evidence set. A proof of correctness is given. 1
All finitely axiomatizable tense logics of linear time flows are coNPcomplete
"... We prove that all finitely axiomatizable tense logics with temporal operators for `always in the future ' and `always in the past ' and determined by linear flows time are coNPcomplete. It follows, for example, that all tense logics containing a density axiom of the form \Lambda n+1 F ..."
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We prove that all finitely axiomatizable tense logics with temporal operators for `always in the future ' and `always in the past ' and determined by linear flows time are coNPcomplete. It follows, for example, that all tense logics containing a density axiom of the form \Lambda n+1 F
Nested Sketches
"... this paper is, to find a functorial model theory for those classes of algebras that appear naturally as semantics of algebraic specifications of parameterized data types, using initial respectively more general free functor semantics, and to extend the functorial model theory to specifications that ..."
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this paper is, to find a functorial model theory for those classes of algebras that appear naturally as semantics of algebraic specifications of parameterized data types, using initial respectively more general free functor semantics, and to extend the functorial model theory to specifications that use as well inductively defined data types as coinductively defined patterns of behavior and their systematic combinations
A Modal Temporal Dynamic Logic Doing The Deadline
, 1997
"... In this paper an investigation into the aspects of formal system specification that manifest themselves when considering both time and system dynamics is carried out. A logic to express temporal dynamic properties is developed. ..."
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In this paper an investigation into the aspects of formal system specification that manifest themselves when considering both time and system dynamics is carried out. A logic to express temporal dynamic properties is developed.
Knowledge, Actions, and Tests
, 1999
"... We study a modal logic of knowledge and action, focussing on epistemic tests. We view an epistemic test as an action undertaken by an agent in order to establish whether a given formula is true. Such tests increase the knowledge of agents. We propose a semantics, and associate an axiomatics and a pr ..."
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We study a modal logic of knowledge and action, focussing on epistemic tests. We view an epistemic test as an action undertaken by an agent in order to establish whether a given formula is true. Such tests increase the knowledge of agents. We propose a semantics, and associate an axiomatics and a proof procedure. 1 Introduction Imagine a robot that wants to open a door that might be locked. If the robot is cute enough, he starts by checking whether the door is effectively locked up. Such test actions are an important form of interaction. They are central e.g. in diagnosis in order to discriminate the possible fault configurations) or in decision under uncertainty. Tests are a onesided form of communication: the agent acquires knowledge about the environment, while that knowledgegathering action does not change the environment. (There are two simplifying hypotheses we make here: first, we suppose that the environment of the agent doesn't change while the test is done; second, we su...
Dynamic Coalgebraic Modalities
"... With this work we aim to place dynamic modal logics such as Propositional Dynamic Logic (PDL) [1] and Game Logic (GL) [4] in a uniform coalgebraic framework. In our view, a dynamic system S consists of the following ingredients: 1. A set S which represents the global states of S. 2. An algebra L of ..."
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With this work we aim to place dynamic modal logics such as Propositional Dynamic Logic (PDL) [1] and Game Logic (GL) [4] in a uniform coalgebraic framework. In our view, a dynamic system S consists of the following ingredients: 1. A set S which represents the global states of S. 2. An algebra L of labels (denoting actions, programs, games,...). 3. An interpretation of labels as Gcoalgebras on the state space S. 4. A collection of labelled modalities [α], for α ∈ L, where intuitively [α]ϕ reads: “after α, ϕ holds”. Formally, the interpretation of labels is a map σ: L → (GS) S which describes how actions change the global system state. The algebraic structure on L describes how one can compose actions into more complex ones. The same type of algebraic structure should be carried by (GS) S, and we say that σ is standard, if σ is an algebra homomorphism, which means that the semantics of actions is compositional. By considering the exponential adjoint ̂σ: S → (GS) L we obtain a behavioural description of the system in the form of a G Lcoalgebra. These two (equivalent) views of a dynamic system form the basis of our modelling. In short, σ describes structure and dynamics, and ̂σ describes behaviour and induces modalities. σ: L → (GS) S (algebraic view: structure, dynamics)
Nested Sketches (Preliminary Version)
"... Since the fundamental work of Lawvere in 1963 [7] it is common to understand a theory as category with additional structure, to understand a model of the ..."
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Since the fundamental work of Lawvere in 1963 [7] it is common to understand a theory as category with additional structure, to understand a model of the