This special issue of the Journal of Logic and Computation contains revised and extended versions of selected papers from LORI-5, the 5th International Workshop on Logic, Rationality and Interaction. LORI-5 was held during 28–31 October 2015, in Taipei, Taiwan, and hosted by the Department of Philosophy of National Taiwan University and the Institute of Philosophy of Mind and Cognition of National Yang-Ming University. The hallmark of the LORI series is its broad topical coverage, putting logic into contact with disciplines as diverse as game theory and decision theory, philosophy and epistemology, linguistics, computer science and artificial intelligence. In the current special issue, the reader will find several mainstays of the LORI series: modal and epistemic logics, theories of learning and argumentation, and pure logic. Out of 62 original submissions to LORI-5, 32 full papers were selected for presentation based on reviews by at least two—and on average three—members of the LORI-5 program committee. After the workshop, the authors of 20 of the full papers were invited to submit extended versions of their papers to be considered for either the present special issue or a parallel special issue of the journal Synthese. Each of the 10 papers considered for this special issue underwent review by two or three referees, leading to at least one—and in some cases two or three—rounds of revision. The final products are the nine papers collected in this issue. As an overview of its contents, below we provide a brief summary of each paper (in alphabetical order by author’s last name). In ‘Modal Logics of Sabotage Revisited’, Guillaume Aucher, Johan van Benthem and Davide Grossi explore model-theoretic and proof-theoretic aspects of the system of sabotage modal logic previously introduced by van Benthem. Motivated by so-called sabotage games, in which players take turns moving through a graph or deleting edges from the graph to hinder the other player, sabotage modal logic adds to basic modal logic a new unary modality $$\blacklozenge$$ with the following semantics: $$\blacklozenge\varphi$$ is true at a state $$w$$ of a relational model if and only if there is some pair $$(w,v)$$ in the relation such that $$\varphi$$ is true at $$w$$ in the new relational model obtained by removing the pair $$(w,v)$$ from the relation. The authors characterize this sabotage modal language, viewed under translation as a fragment of the language of first-order logic, as the fragment of the first-order language that is invariant with respect to a natural notion of sabotage bisimulation. They then turn to reasoning in sabotage modal logic, providing a sound and complete semantic tableaux system and associated labelled sequent calculus. Finally, the authors provide a wealth of further perspectives and open problems concerning sabotage modal logic. In ‘Symbolic Model Checking for Dynamic Epistemic Logic—S5 and Beyond’, Johan van Benthem, Jan van Eijck, Malvin Gattinger and Kaile Su start with the observation that existing implementations for Dynamic Epistemic Logic (DEL) are rather ad hoc. Their aim is to bring to DEL the best model-checking and techniques based on satisfiability solvers available in computational logic. To do so, they introduce a representation of DEL models as so-called knowledge structures, which allow for symbolic model checking. Parallel to this, they develop knowledge transformers, the analogue of action models in DEL. Using this machinery, the authors show that they can solve some well-known benchmark problems in DEL faster than existing methods; they compare their approach to model checking for temporal logics; and they make a case that their method raises issues regarding logical representation and update. All source code for their model checker, technical documentation and a simple web interface is publicly available. In ‘Learning to Act: Qualitative Learning of Deterministic Action Models’, Thomas Bolander and Nina Gierasimczuk bring the perspective of learning theory to bear on DEL. In DEL, an initial epistemic model representing the knowledge of several agents can be updated by an action model representing an informational event, resulting in a new epistemic model representing the knowledge of the agents after the event. A natural learning-theoretic question in this context is whether by observing pairs of the form (initial epistemic state, resulting epistemic state), one can infer the action model responsible for these changes. The authors analyse this problem in detail, according to the criterion of finite identifiability, which requires conclusively inferring the correct action model in a finite amount of time, as well as the criterion of identifiability in the limit, which only requires inconclusive convergence to the correct action model. In ‘Decidable Temporal and Sequential Relevant Logics’, Norihiro Kamide introduces two new temporal logics based on the relevant logic RW$$^+$$. The main motivations for developing such systems concern the formalization of inferences that are closer to human reasoning, as well as a number of possible applications in computer science. The author introduces a Gentzen-type sequent calculus STRW for a new temporal relevant logic TRW, which introduces temporal operators on top of the positive contractionless relevant logic RW$$^+$$. In addition, Kamide introduces a Gentzen-type sequent calculus SSRW for a new sequential relevant logic SRW, which introduces a sequence modal operator on top of RW$$^+$$. Finally, it is demonstrated that both STRW and SSRW have the properties of cut-elimination, completeness and decidability. In ‘Tableaux for a Combination of Propositional Dynamic Logic and Epistemic Logic with Interactions’, Yanjun Li investigates a fusion of two important logical frameworks. Propositional dynamic logic is a logic for reasoning about programs or actions. Epistemic logic is a logic for reasoning about agent’s beliefs and knowledge. The combination of these logics is therefore a powerful tool for reasoning about interactions between knowledge and actions. Li presents a tableau-based decision procedure for deciding satisfiability with respect to single-agent models with the properties of perfect recall and no miracles, and Li proves this procedure to be sound and complete. In ‘Formulating Semantics of Probabilistic Argumentation by Characterizing Subgraphs: Theory and Empirical Results’, Beishui Liao, Kang Xu and Huaxin Huang criticize existing approaches to the semantics of probabilistic argumentation as inefficient or infeasible. These approaches equate the probability of a set E of arguments being an extension with the sum of the probabilities of all subgraphs each of which has the extension E. The authors address the problems with this approach from two perspectives: (i) conceptually, they define specific properties to characterize the subgraphs of a probabilistic argument graph with respect to a given extension such that the probability of E’s being an extension can be defined in terms of these properties; and (ii) computationally, they take preferred semantics as an example and develop algorithms to evaluate the efficiency of their approach. The paper shows that their proposed approach not only dramatically decreases the time for computing the probability of E’s being an extension, but also has an additional attractive property. In ‘On the ‘Transitivity’ of Consequence Relations’, David Ripley investigates different properties of logical consequence relations that have been called ‘transitivity’, as well as variations on such properties. Ripley considers consequence relations between a set of premises and a single conclusion (the Set-Frml framework), as well as consequence relations between a set of premises and a set of conclusions (the Set-Set framework), where the premises are understood conjunctively and the conclusions disjunctively. The result of Ripley’s analysis is a thorough catalogue of implications between different transitivity-like properties of consequence relations. Ripley concludes that when logicians speak of a ‘transitive’ consequence relation, ‘it behooves us to make clear exactly what we are saying; there is no single thing we must obviously mean’. We hope that these papers will not only advance the state of the art on their respective topics, but also provide for those unable to attend LORI-5 a sense of the stimulating diversity of the workshop. © The Author, 2017. Published by Oxford University Press. All rights reserved. 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Journal of Logic and Computation – Oxford University Press
Published: Mar 1, 2018
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