Related papers: Hierarchies in Dependence Logic
We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindstr\"om, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the…
We stratify intuitionistic first-order logic over $(\forall,\to)$ into fragments determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy). We study the decidability and complexity of these…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
This paper is motivated by the desire to study package management using the toolkit of the semantics of functional languages. As it transpires, this is deeply related to the semantics of concurrent computation. The models we produce are not…
This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…
Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers \forall p, \exists p over propositions. In the context of Kripke semantics, a proposition is a subset of the worlds in a…
Some new formulas for the KP hierarchy are derived from the differential Fay identity. They proved to be useful for the $k$-constrained hierarchies providing a series of determinant identities for them. A differential equation is introduced…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Subobject independence as morphism co-possibility has recently been defined in [2] and studied in the context of algebraic quantum field theory. This notion of independence is handy when it comes to systems coming from physics, but when…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
A semantic embedding of (constant domain) quantified conditional logic in classical higher-order logic is presented.
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In…