Guards, Bounds, and Generalized Semantics

Guards, Bounds, and Generalized Semantics

Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary firstorder formulas. In particular, we give a new straightforward reduction from the former no...

A generalized fortress problem using k-consecutive vertex guards

UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

Well-Founded Semantics, Generalized

Classical fixpoint semantics for logic programs is based on the TP immediate consequence operator. The Kripke/Kleene, three-valued, semantics uses ΦP , which extends TP to Kleene’s strong three-valued logic. Both these approaches generalize to cover logic programming systems based on a wide class of logics, provided only that the underlying structure be that of a bilattice. This was presented i...

A generalized inquisitive semantics.∗

In Inquisitive Semantics, formulas are evaluated on ordered pairs of indices; actually, the order of the pair is irrelevant, so these pairs could just just as well be taken to be non-empty sets of indices of cardinality at most two. This last restriction, however, sounds particularly unnatural, especially considering that the definition of inquisitive semantics can be easily reformulated in suc...