•  395
    From BDI and stit to bdi-stit logic
    with Caroline Semmling
    Logic 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
  •  202
    Normative Verantwortung für Handlungen Anderer. Eine Untersuchung im Rahmen der stit -Theorie
    with Sarah Ganter
    Facta Philosophica 7 (2): 167-187. 2005.
  •  105
    The Slingshot Argument and Sentential Identity
    with Yaroslav Shramko
    Studia Logica 91 (3): 429-455. 2009.
    The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false . In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.Wóitowicz and put to the test her claim that the slingshot argument is in …Read more
  •  102
    Some Useful 16-Valued Logics: How a Computer Network Should Think
    with Yaroslav Shramko
    Journal of Philosophical Logic 34 (2): 121-153. 2005.
    In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = (2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᵍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an information ordering together with a truth o…Read more
  •  88
    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
  •  85
    Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particu…Read more
  •  81
    Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System
    with Yaroslav Shramko
    Studia Logica 88 (3): 405-429. 2008.
    According to Suszko's Thesis, there are but two logical values, true and false. In this paper, R. Suszko's, G. Malinowski's, and M. Tsuji's analyses of logical two-valuedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation.
  •  80
    Doxastic Decisions, Epistemic Justification, and The Logic of Agency
    Philosophical Studies 128 (1): 201-227. 2006.
    A prominent issue in mainstream epistemology is the controversy about doxastic obligations and doxastic voluntarism. In the present paper it is argued that this discussion can benefit from forging links with formal epistemology, namely the combined modal logic of belief, agency, and obligation. A stit-theory-based semantics for deontic doxastic logic is suggested, and it is claimed that this is helpful and illuminating in dealing with the mentioned intricate and important problems from mainstrea…Read more
  •  78
    Contradiction and contrariety. Priest on negation
    Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1): 81-93. 2006.
    Although it is not younger than other areas of non-classical logic, paraconsistent logic has received full recognition only in recent years, largely due to the work of, among others, Newton da Costa, Graham Priest, Diderik Batens, and Jerzy Perzanowski. A logical system Λ is paraconsistent if there is a set of Λ-formulas Δ ∪ {A} such that in Λ one may derive from Δ both A and its negation, and the deductive closure of Δ with respect to Λ is different from the set of all formulas. If from Δ one m…Read more
  •  77
    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
  •  75
    Hyper-contradictions, generalized truth values and logics of truth and falsehood
    with Yaroslav Shramko
    Journal of Logic, Language and Information 15 (4): 403-424. 2006.
    In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining a…Read more
  •  72
    Logical Connectives for Constructive Modal Logic
    Synthese 150 (3): 459-482. 2006.
    Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.
  •  66
    This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.
  •  62
    Sequent calculi for some trilattice logics
    with Norihiro Kamide
    Review 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
  •  59
    Constructive negation, implication, and co-implication
    Journal of Applied Non-Classical Logics 18 (2-3): 341-364. 2008.
    In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.
  •  55
    Diamonds are a philosopher's best friends
    Journal of Philosophical Logic 31 (6): 591-612. 2002.
    The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived …Read more
  •  51
    External Curries
    Journal 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
  •  45
    Connectives stranger than tonk
    Journal of Philosophical Logic 35 (6). 2006.
    Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a numbe…Read more
  •  44
    The Power of Belnap: Sequent Systems for SIXTEEN ₃ (review)
    Journal of Philosophical Logic 39 (4). 2010.
    The trilattice SIXTEEN₃ is a natural generalization of the wellknown bilattice FOUR₂. Cut-free, sound and complete sequent calculi for truth entailment and falsity entailment in SIXTEEN₃, are presented
  •  44
    Informational interpretation of substructural propositional logics
    Journal 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.
  •  39
    Nested 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.
  •  38
    Consequence, Counterparts and Substitution
    The Monist 85 (4): 483-497. 2002.
  •  37
    Substructural logics
    Erkenntnis 45 (1): 115-118. 1996.
  •  36
    Editorial Introduction. Truth Values: Part I (review)
    with Yaroslav Shramko
    Studia Logica 91 (3): 295-304. 2009.
  •  36
    Editorial Introduction. Truth Values: Part II (review)
    with Yaroslav Shramko
    Studia Logica 92 (2): 143-146. 2009.
  •  36
    Reprint of: A more general general proof theory
    Journal of Applied Logic 25 23-46. 2017.
    In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction pro…Read more