-
97A general possible worlds framework for reasoning about knowledge and beliefStudia Logica 49 (4). 1990.In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek a…Read more
-
67External CurriesJournal of Philosophical Logic 44 (4): 453-471. 2015.Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In t…Read more
-
419From BDI and stit to bdi-stit logicLogic and Logical Philosophy 17 (1-2): 185-207. 2008.Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascripti…Read more
-
22Tarskian Structured Consequence Relations and Functional CompletenessMathematical Logic Quarterly 41 (1): 73-92. 1995.In this paper functional completeness results are obtained for certain positive and constructive propositional logics associated with a Tarski-type structured consequence relation as defined by Gabbay
-
5Action-Theoreticaspects of Theory ChoiceIn S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science, Kluwer Academic Publisher. pp. 419--435. 2004.
-
38Predicate logics on displayStudia Logica 62 (1): 49-75. 1999.The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not the…Read more
-
53Informational interpretation of substructural propositional logicsJournal of Logic, Language and Information 2 (4): 285-308. 1993.This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.
-
Thomas Andreas Meyer, Willem Adrian Labuschagne, and Johannes heidema/refined espistemic entrenchment 237-259Journal of Logic, Language, and Information 9 (2): 139. 1992.
-
1Displaying the Modal Logic of ConsistencyJournal of Symbolic Logic 64 (4): 1573-1590. 1999.It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.
-
38The Logic of Generalized Truth Values and the Logic of BilatticesStudia Logica 103 (1): 91-112. 2015.This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive bil…Read more
-
42Correction to ‘Displaying the modal logic of consistency’Journal of Symbolic Logic 68 (2): 712-712. 2003.
-
77Sequent calculi for some trilattice logicsReview of Symbolic Logic 2 (2): 374-395. 2009.The trilattice SIXTEEN3 introduced in Shramko & Wansing (2005) is a natural generalization of the famous bilattice FOUR2. Some Hilbert-style proof systems for trilattice logics related to SIXTEEN3 have recently been studied (Odintsov, 2009; Shramko & Wansing, 2005). In this paper, three sequent calculi GB, FB, and QB are presented for Odintsovs coordinate valuations associated with valuations in SIXTEEN3. The equivalence between GB, FB, and QB, the cut-elimination theorems for these calculi, and…Read more
-
20Bemerkungen Zur Semantik Nicht‐Normaler Möglicher WeltenMathematical Logic Quarterly 35 (6): 551-557. 1989.
-
11Review: Review of Modal Logic P. Blackburn, M. de Rijke, Y. Venema: Review of Modal Logic (review)Logic Journal of the IGPL 10 (4): 457-458. 2002.
-
47Semantics-based Nonmonotonic InferenceNotre Dame Journal of Formal Logic 36 (1): 44-54. 1995.In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic base system by Kleene's three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson's constructive logic N instead of intuitionistic logic or Kleene's system. Moreover, in N a more general notion of consistency can be defined …Read more
-
47Nested deontic modalities: Another view of parking on highways (review)Erkenntnis 49 (2): 185-199. 1998.A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions. In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities.
-
30Hypersequent and Display Calculi – a Unified PerspectiveStudia Logica 102 (6): 1245-1294. 2014.This paper presents an overview of the methods of hypersequents and display sequents in the proof theory of non-classical logics. In contrast with existing surveys dedicated to hypersequent calculi or to display calculi, our aim is to provide a unified perspective on these two formalisms highlighting their differences and similarities and discussing applications and recent results connecting and comparing them.
-
103A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and FalsityTopoi 31 (1): 93-100. 2012.Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is to…Read more
-
10Editorial introduction. Special issue on consequence relations and sequent systemsLogic Journal of the IGPL 6 (3): 377-381. 1998.
-
6Reasoning About Belief RevisionIn Erik J. Olson Sebastian Enqvist (ed.), Belief Revision Meets Philosophy of Science, Springer. pp. 303--328. 2011.
-
5We study a propositional bimodal logic consisting of two S4 modalities £ and [a], together with the interaction axiom scheme a £ϕ → £ aϕ. In the intended semantics, the plain £ is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation a. The interaction axiom expresses the property that the Ra relation is lower semi-continuous with respect to the topology. The c…Read more
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |
Areas of Interest
Philosophy of Language |