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Substructural Logics on Display
, 1998
"... Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek ca ..."
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Cited by 49 (16 self)
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Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek calculus, which contains these multiple connectives, and obtain numerous logics like: exponentialfree linear logic, relevant logic, BCK logic, and intuitionistic logic, in an incremental way. Each of these logics also has a classical counterpart, and some also have a "cyclic" counterpart. These logics have been studied extensively and are quite well understood. Generalising further, one can start with intuitionistic BiLambek logic, which contains the dual of every connective from the Lambek calculus. The addition of the structural rules then gives Bilinear, Birelevant, BiBCK and Biintuitionistic logic, again in an incremental way. Each of these logics also has a classical counterpart, and som...
Free Variable Tableaux for Propositional Modal Logics
 TABLEAUX97, LNCS 1227
, 1997
"... We present a sound, complete, modular and lean labelled tableau calculus for many propositional modal logics where the labels contain "free" and "universal" variables. Our "lean" Prolog implementation is not only surprisingly short, but compares favourably with other co ..."
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Cited by 47 (5 self)
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We present a sound, complete, modular and lean labelled tableau calculus for many propositional modal logics where the labels contain "free" and "universal" variables. Our "lean" Prolog implementation is not only surprisingly short, but compares favourably with other considerably more complex implementations for modal deduction.
Epistemic logic and information update
 In P. Adriaans
, 2008
"... Epistemic logic investigates what agents know or believe about certain factual descriptions of the world, and about each other. It builds on a model of what information is (statically) available in a given system, and isolates general principles concerning knowledge and belief. The information in a ..."
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Cited by 26 (5 self)
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Epistemic logic investigates what agents know or believe about certain factual descriptions of the world, and about each other. It builds on a model of what information is (statically) available in a given system, and isolates general principles concerning knowledge and belief. The information in a system may well change as a result of various changes: events from the outside, observations by the agents, communication between the agents, etc. This requires information updates. These have been investigated in computer science via interpreted systems; in philosophy and in artificial intelligence their study leads to the area of belief revision. A more recent development is called dynamic epistemic logic. Dynamic epistemic logic is an extension of epistemic logic with dynamic modal operators for belief change (i.e., information update). It is the focus of our contribution, but its relation to other ways to model dynamics will also be discussed in some detail. Situating the chapter This chapter works under the assumption that knowledge is a variety of true justifiable belief. The suggestion that knowledge is nothing but true justified belief is very old in philosophy, going back to Plato if not further. The picture is that we are faced with alternative “worlds”, including perhaps our own world but in addition other
Fibring Labelled Deduction Systems
 Journal of Logic and Computation
, 2002
"... We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial ..."
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Cited by 16 (9 self)
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We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial characterization of fibring of models. Based on this, we establish the conditions under which our systems are sound and complete with respect to the general semantics for the corresponding logics, and establish requirements on logics and systems so that completeness is preserved by both forms of fibring.
Fibred Tableaux for MultiImplication Logics
, 1996
"... . We investigate the notion of bred tableaux which naturally arises from the idea of bred semantics. Dierent implication operators peacefully cohabit and cooperate within the same labelled tableau method. 1 Introduction The last decade has seen a proliferation of dierent logical systems proposed f ..."
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Cited by 7 (3 self)
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. We investigate the notion of bred tableaux which naturally arises from the idea of bred semantics. Dierent implication operators peacefully cohabit and cooperate within the same labelled tableau method. 1 Introduction The last decade has seen a proliferation of dierent logical systems proposed for a variety of dierent purposes, both theoretical and practical. These logics appear to satisfy the needs of dierent application areas or to capture dierent interpretations of the logical operators. This is particularly apparent in the case of the conditional operator. All the dierent implication logics which have been proposed in the literature seem to succeed in modelling some aspect of the ordinary use of this operator, or in suggesting useful nonstandard interpretations. What emerges from these developments is a class of operators bearing a family resemblance to each other, each of which may t a dierent application. So, a crucial problem, both in pure and applied logic, is th...
Freevariable tableaux for propositional modal logics
 Studia Logica
"... Abstract. Freevariable semantic tableaux are a wellestablished technique for firstorder theorem proving where free variables act as a metalinguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional m ..."
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Cited by 5 (0 self)
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Abstract. Freevariable semantic tableaux are a wellestablished technique for firstorder theorem proving where free variables act as a metalinguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including nontrivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.
Fibred modal tableaux (preliminary report
 Tilburg University
, 1998
"... Abstract. We describe a general and uniform tableau methodology for multimodal logics arising from Gabbay’s methodology of fibring and Governatori’s tableau system KEM. 1 ..."
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Cited by 1 (1 self)
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Abstract. We describe a general and uniform tableau methodology for multimodal logics arising from Gabbay’s methodology of fibring and Governatori’s tableau system KEM. 1
A ResourceSensitive Account of the Use of Artifacts (Extended Abstract)
"... ABSTRACT The aim of this abstract is to introduce a formal framework enabling to reason about resourcesensitive uses of artifacts. To achieve this, we integrate (nonnormal) modalities into Intuitionistic Linear Logic. The function of an artifact is a (resourcesensitive) linear implication and we ..."
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ABSTRACT The aim of this abstract is to introduce a formal framework enabling to reason about resourcesensitive uses of artifacts. To achieve this, we integrate (nonnormal) modalities into Intuitionistic Linear Logic. The function of an artifact is a (resourcesensitive) linear implication and we interpret each modality as an agent's bringing about of resources. Categories and Subject Descriptors General Terms Theory Keywords Artifacts, Functions, Linear Logic, Modalities, Proof Theory PROPOSAL DESCRIPTION Artifacts are special kind of objects that are characterized by the fact that they are designed by some agent in order to achieve a goal in a particular environment. An important aspect of the modelisation of artifacts is their interaction with the environment and with the agents that use the artifact to achieve a specific goal Language and sequent calculus IMLL. The language of IMLL LIMLL is defined by the BNF A :: A, where p ∈ Atom. The resourcesensitive flavor of IMLL is due to the lack of structural rules in the sequent calculus, namely IMLL rejects the global validity of weakening (that amounts to a monotonicity of the entailment) and contraction, that are responsible for example of tautology such as A → A ∧ A in classical logic; the counterpart in IMLL A A ⊗ A is no longer valid. Exchange still holds, thus contexts of formulas are multisets. The proofsearch complexity of IMLL NPcomplete Models of IMLL. We introduce a Kripkelike model for IMLL that is basically due to Urquhart