Possible Worlds Semantics for Indicative and Counterfactual Conditionals?

Stit-LOGIC FOR IMAGINATION EPISODES WITH VOLUNTARY INPUT

“…Special Transitivity. Berto admits "[i]t may be, however, that there are intuitive counterexamples to ST, forceful enough to lead us to reject PIE" for PIE entails Substitutivity, which, in turn, entails ST. For potential counterexamples to ST we refer to (potential) counterexamples to Cautious Cut [62], a principle of conditional logic, which also has an analogue in terms of the consequence relation in non-monotonic logic [59].…”

“…To ensure this, we employ general frames the role of which is exactly to ensure that all/the right truth-sets are "available." General frames are a standard tool in modal logic [13] and have been applied in the context of conditional logics [20,21,57,62,63,68]. General frames in our setting contain an element P, which is a set of subsets of MH (Tree), the role of which is to ensure that for each formula that can feature as antecedent of formulas of the form A 2→ B its truth-set is in P. As per our syntactic restriction, formulas of the form A 2→ B cannot have formulas of the same form in the antecedent.…”

“…The combined approaches lead to a semantics that (in)validates analogues of the desired (in)validities from Berto [9]. The semantics improves on Berto's approach in the following ways: (i) it explicitly models the agent's deliberate choice of the initial input of an imaginative episode, (ii) in a multi-agent setting, (iii) provides a purely structural correspondence theory due to employing Chellas-Segerberg semantics for the conditional operator [20,21,57,62,63,68], which in turn (iv) provides the possibility of dropping some potentially debatable axioms.…”

Connexive Conditional Logic. Part I

“…David Nelson's paraconsistent constructive logic [Almukdad and Nelson, 1984] C paraconsistent constructive connexive logic [Wansing, 2005] CK basic conditional logic [Chellas, 1975;Segerberg, 1989;Unterhuber, 2013;Unterhuber and Schurz, 2014] CKR conditional logic CK extended by A A (reflexivity) ( [Unterhuber, 2013, Ch. 7.1]; see also [Chellas, 1975;Segerberg, 1989;Unterhuber and Schurz, 2014]) This paper CK FDE basic conditional logic CK based on FDE 6 CKR FDE conditional logic CKR based on FDE cCL basic weakly connexive conditional logic CCL basic connexive conditional logic, cCL extended by A A cCCL basic weakly connexive constructive conditional logic CCCL basic connexive constructive conditional logic, cCCL extended by A A Table 1.…”

“…We shall sometimes omit outermost brackets of formulas. 7 As in [Unterhuber, 2013;Unterhuber and Schurz, 2014], in addition to L we shall use a language L FC for talking about (general) frame conditions. The language L FC is a two-sorted, set-theoretic language which contains (i) variables w, w ′ , w ′′ , .…”