Extended Modal Dependence Logic $\mathcal{EMDL}$

Approximation and dependence via multiteam semantics

“…From (6) it follows that θ is well-defined, whereas (5) and (7) ensure that every clause of ϕ is satisfied by θ. Hence we have ϕ ∈ 3SAT.…”

“…Here one would just explicitly state the number of rows to be removed from the team, i.e., setting p to m in the constructed formula in the proof of Theorem 3. Regarding Theorem 4 in this setting the formula f (ϕ) increases the number of clauses by factor 10 and therefore requires to set p to 7 10 · 10 · m = 7 · m where m is the number of clauses of the given 3CNF formula ϕ.…”

“…The study of modal dependence logic was initiated by Väänänen [37] in 2008. Shortly after, extended modal dependence logic was introduced by Ebbing et al [7] and modal independence logic by Kontinen et al [27]. In purely propositional context the study was initiated by Yang and Väänänen [42] and further studied, e.g., by Hannula et al [17].…”

Modal dependence logics: axiomatizations and model-theoretic properties

“…, α n , β) with classical arguments are often referred to as extended dependence atoms. It is proved in [7,12] that MD is strictly less expressive than MD + , and the latter has the same expressive power as MD ∨ .…”

Supervenience, Dependence, Disjunction

“…37 Ciardelli in [2016a;2016b]  though not in [Ciardelli and Roelofsen, 2011] 38  uses the notation ϕ ψ for Väänä-nen's ϕ ∨ B ψ, calling the connective concerned inquisitive disjunction. (It is called ) We will look at some aspects of the behaviour of this and other connectives in the setting of inquisitive logic in Section 6, and here offer one suggestion as to something evidently puzzling Ciardelli at p. 235 of [2016a], when he cites Ebbing et al [2013] as discussing inquisitive disjunction and writes parenthetically "which they refer to, curiously, as classical disjunction". The suggestion is that the usual presumption or convention that the metalogic for discussions of various ('object') logics is to be classical logic, so whenever the clause governing compounds formed by a particular in the inductive definition of a relation 36 Is the use of the tensor notation familiar from linear logic coincidental here?…”