Tero Tulenheimo

The present paper provides novel results on the model theory of Independence friendly modal logic. We concentrate on its particularly well-behaved fragment that was introduced in Tulenheimo and Sevenster (Advances in Modal Logic, 2006). Here we refer to this fragment as ‘Simple IF modal logic’ (IFML s ). A model-theoretic criterion is presented which serves to tell when a formula of IFML s is not equivalent to any formula of basic modal logic (ML). We generalize the notion of bisimulation familiar from ML; the resulting asymmetric simulation concept is used to prove that IFML s is not closed under complementation. In fact we obtain a much stronger result: the only IFML s formulas admitting their classical negation to be expressed in IFML s itself are those whose truth-condition is in fact expressible in ML

When discussing knowledge, two relations are of interest: justified doxastic accessibility \ , she is in \ ) and justification equivalence \ exactly the same justified beliefs that she has in \ ). Speaking of compatibility with the agent’s justified beliefs is potentially ambiguous: either of the two relations \ or \ can be meant. I discuss the possibility of identifying the relation of epistemic accessibility \ , she is in \ ) with the union of \ and \ . Neither Gettier’s examples nor the ‘fake barn’ cases contradict this identification. However, the proposal leads to justification equivalent scenarios being symmetric with respect to knowledge: we cannot know a true proposition in a scenario if it is false in a justification equivalent scenario. This analysis may appear to render non-trivial knowledge impossible. This conclusion follows if the extra premise is granted that for all relevant true propositions there is a justification equivalent scenario in which the proposition is false. I provide a meaning-theoretic argument against this premise. I conclude by pointing out problems that would ensue from giving up the proposed connection between \ , \ and \ and allowing asymmetry of justification equivalent scenarios relative to knowledge

Typical applications of Hintikka’s game-theoretical semantics give rise to semantic attributes—truth, falsity—expressible in the $\Sigma^{1}_{1}$-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, $L_{1}$ and $L_{2}$, in both of which two negation signs are available: $\rightharpoondown $ and $\sim$. The latter is the usual GTS negation which transposes the players’ roles, while the former will be interpreted via the notion of mode. Logic $L_{1}$ extends independence-friendly logic; $\rightharpoondown $ behaves as classical negation in $L_{1}$. Logic $L_{2}$ extends $L_{1}$, and it is shown to capture the $\Sigma^{2}_{1}$-fragment of third-order logic. Consequently the classical negation remains inexpressible in $L_{2}$

G. H. von Wright proposed that a temporal interval exemplifies a real contradiction if at least one part of any division of this interval involves the presence of contradictorily related (though non-simultaneous) states. In connection with intervals, two negations must be discerned: 'does not hold at an interval' and 'fails throughout an interval'. Von Wright did not distinguish the two. As a consequence, he made a mistake in indicating how to use his logical symbolism to express the notion of real contradiction. The present paper aims to reconstruct and philosophically motivate von Wright's argument for the possibility of real contradictions.

In Prior’s tense-logical analysis, we can avoid mentioning instants in our language by construing them as propositions of a special kind. Instead of qualifying instants by predicates, we may qualify propositions by modalities. Prior shows that by changing the informal interpretation of our modal-like language, we can similarly attempt to avoid ontological commitments to worlds and even to selves and other bona fide individuals. As he notes, the paraphrasing strategy works too generally to be of direct metaphysical use. I wish to speak of several types of entities within one and the same language. This leads to the issue of cross-context identity: how to make sense of speaking of the same entity of one type relative to distinct entities of another type. My analysis employs the notion of world line. I discern a structure of mutually interrelated categories with three informal interpretations: tense, modal and egocentric. They correspond to different metaphysical views on the interrelations of time, logical alternatives and individuals. Prior’s dilemma regarding the possibility of modalizing, not only our talk concerning times and worlds, but even our discourse pertaining to the ‘real world of individuals’ does not vanish but reappears also in my setting.