Judgment aggregation studies how to aggregate individual judgments on logically correlated propositions into collective judgments. Different logics can be used in judgment aggregation, for which Dietrich and Mongin have proposed a generalized model based on general logics. Despite its generality, however, all nonmonotonic logics are excluded from this model. This paper argues for using nonmonotonic logic in judgment aggregation. Then it generalizes Dietrich and Mongin’s model to incorporate a large class of nonmonotonic logics. This generalization broadens the theoretical boundaries of (...) judgment aggregation by proving that, even if these nonmonotonic logics are employed, certain typical impossibility results still hold. (shrink)

We generalize Ripley’s results on the transitivity of consequence relation, without assuming a logic to be monotonic. Following Gabbay, we assume nonmonotonic consequence relation to be inclusive and cautious monotonic, and figure out the implications between different forms of transitivity of logical consequence. Weaker frameworks without inclusiveness or cautious monotonicity are also discussed. The paper may provide basis for the study of both non-transitive logics and nonmonotonic ones.

Motivated by supplying a new strategy for connexive logic and a better semantics for conditionals so that negating a conditional amounts to negating its consequent under the condition, we propose a new semantics for connexive conditional logic, by combining Kleene’s three-valued logic and a slight modification of Stalnaker’s semantics for conditionals. In the new semantics, selection functions for selecting closest worlds for evaluating conditionals can be undefined. Truth and falsity conditions for conditionals are then supplemented with a precondition that the (...) selection function is defined. Based on the new semantics, we define six conditional logics by different classes of models, using two notions of validity, one preserving truth and the other preserving tolerant truth. We prove soundness and completeness of these logics and compare them with some conditional logics in the literature. Our partial function plus precondition strategy may be used in other semantic frameworks to generate more connexive logics. (shrink)

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial (...) solution to the paradox of analysis. (shrink)

First we show that the classical two-player semantic game actually corresponds to a three-valued logic. Then we generalize this result and give an n-player semantic game for an n + 1-valued logic with n binary connectives, each associated with a player. We prove that player i has a winning strategy in game G if and only if the truth value of φ is $t_i $ in the model M, for 1 ≤ i ≤ n; and none of the players has (...) a winning strategy in G if and only if the truth value of φ is $t_o $ in M. (shrink)

Constant conjunction theory of causation had been the dominant theory in philosophy for a long time and regained attention recently. This paper gives a logical framework of causation based on the theory. The basic idea is that causal statements are empirical, and are derived from our past experience by observing constant conjunction between objects. The logic is defined on linear time structures. A causal statement is evaluated at time points, such that its value depends on what has been in the (...) past. We first give a semantics that contains basic conditions that, we think, must hold for a concept of causation, on which we define the minimal causal logic. Then we discuss its possible extensions for various concepts of causation. Complete deductive systems are given. (shrink)

In modal logic, semantic consequence is usually defined locally by truth preservation at all worlds in all models. It can also be defined globally by truth preservation in all models. The latter is called global consequence, which is much less studied than the standard local one. In this paper we first study the relationship between local and global consequence. Then we give some correspondence results for global consequence. Finally, we illustrate two applications of global consequence, connecting it with informational consequence (...) and update consequence proposed in formal semantics. Some results in the paper are already known, which are collected in the paper for the sake of completeness. The others appear to be new. We suggest that global consequence is not only interesting theoretically, but also useful for applications. (shrink)

Most nonmonotonic logics are assumed to be cumulative, which is often regarded as the minimum requirement for a logic. We argue that cumulativity, in particular, cumulative transitivity can be abandoned, in order to better characterize reasoning in uncertainty. But giving up cumulative transitivity makes it hard to obtain representation results for these logics. Borrowing the idea from strict-tolerant logics, we give some representation results for nonmonotonic logics that are not cumulatively transitive.

We associate the semantic game with chance moves conceived by Blinov with Blamey’s partial logic. We give some equivalent alternatives to the semantic game, some of which are with a third player, borrowing the idea of introducing the pseudo-player called Nature in game theory. We observe that IF propositional logic proposed by Sandu and Pietarinen can be equivalently translated to partial logic, which implies that imperfect information may not be necessary for IF propositional logic. We also indicate that some independent (...) quantifiers can be regarded as dependent quantifiers of indeterminate sequence, using the interjunction connective in partial logic. We conclude our paper by indicating some further research in a more general setting. (shrink)

We construct a Hilbert style system RPL for the notion of plausibility measure introduced by Halpern J, and we prove the soundness and completeness with respect to a neighborhood style semantics. Using the language of RPL, we demonstrate that it can define well-studied notions of necessity, conditionals and propositional identity.