Herbrand Theorems for Substructural Logics

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classes of formulas.

Skolemization for Substructural Logics

The usual Skolemization procedure, which removes strong quantifiers by introducing new function symbols, is in general unsound for first-order substructural logics defined based on classes of complete residuated lattices. However, it is shown here (following similar ideas of Baaz and Iemhoff for first-order intermediate logics in [1]) that first-order substructural logics with a semantics satisfying certain witnessing conditions admit a “parallel” Skolemization procedure where a strong quantifier is removed by introducing a finite disjunction or conjunction (as appropriate) of formulas with multiple new function symbols. These logics typically lack equivalent prenex forms. Also, semantic consequence does not in general reduce to satisfiability. The Skolemization theorems presented here therefore take various forms, applying to the left or right of the consequence relation, and to all formulas or only prenex formulas.

Torn between state and market: Private policy implementation and conflicting institutional logics

Policy implementation by private actors constitutes a “missing link” for understanding the implications of private governance. This paper proposes and assesses an institutional logics framework that combines a top-down, policy design approach with a bottom-up, implementation perspective on discretion. We argue that the conflicting institutional logics of the state and the market, in combination with differing degrees of goal ambiguity, accountability and hybridity play a crucial role for output performance. These arguments are analyzed based on a secondary analysis of seven case studies of private and hybrid policy implementation in diverging contexts. We find that aligning private output performance with public interests is at least partly a question of policy design congruence: private implementing actors tend to perform deficiently when the conflicting logics of the state and the market combine with weak accountability mechanisms.

How Much am I Expected to Pay for my Parents‘ Firm? An Institutional Logics Perspective on Family Discounts

Recent evidence suggests that successors do not simply inherit their parents’ firm, but have to pay a certain price. Building on institutional logics literature, we explore successors’ family discount expectations, defined as the rebate expected from parents in comparison to nonfamily buyers when assuming control of the firm. We find that family cohesion increases discount expectations, while successors’ fear of failure and family equity stake in the firm decrease discount expectations. Higher education in business or economics weakens These effects. On average, in our study comprised of 16 countries, successors expect a 57% family discount.

Realizing public announcements by justifications

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present OPAL(K) and JPAL(K) , two alternative justification counterparts of Gerbrandy–Groeneveld's public announcement logic PAL(K) . We show that PAL(K) is the forgetful projection of both OPAL(K) and JPAL(K) . We also establish that JPAL(K) partially realizes PAL(K) . The question whether a similar result holds for OPAL(K) is still open.

Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics.