The Expressive Power of Modal Dependence Logic

We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended with intuitionistic disjunction. Furthermore, we show that the expressive power of modal logic with intuitionistic disjunction and extended modal dependence logic coincide. Finally we establish that any translation from extended modal dependence logic into modal logic with intuitionistic disjunction increases the size of some formulas exponentially.Comment: 19 page

Axiomatizing propositional dependence logics

We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and modal logic. In addition, we give novel labeled tableau calculi for PD, MDL, and EMDL. We prove soundness, completeness and termination for each of the labeled calculi

Semantic Incompleteness of del Cerro and Herzig's Hilbert System for a Combination of Classical and Intuitionistic Propositional Logic

This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system (C+J)- is semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979)

Semantic Incompleteness of Hilbert System for a Combination of Classical and Intuitionistic Propositional Logic

This paper shows Hilbert system $(\mathbf{C+J})^{-}$, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system $(\mathbf{C+J})^{-}$ contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system $(\mathbf{C+J})^{-}$ is semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979).Comment: 9 page

Conditional independence and biscuit conditional questions in Dynamic Semantics

Biscuit conditionals such as If you are thirsty, there's beer in the fridge are felt different from canonical conditionals such as If it's raining, the fireworks will be cancelled in that the consequent seems to be entailed regardless of the truth/falsity of the antecedent. Franke (2009) argues that the "feeling of the consequent entailment" in biscuit conditionals is due to the conditional independence between the antecedent and consequent; thus a uniform semantics for canonical and biscuit conditionals can be maintained. A question arises as to whether it is possible to derive the same consequent entailment in the framework of dynamic semantics. Furthermore, there are some instances of biscuit conditional questions such as If I get thirsty, is there anything in the fridge? This paper provides a dynamic and non-symmetric version of the independence condition, a d-independence condition which correctly derives the consequent entailment in both declaratives and interrogatives