Related papers: A logic of co-valuations
By Lindstr\"{o}m's theorems, the expressive power of first order logic (and similarly continuous logic) is not strengthened without losing some interesting property. Weakening it, is however less harmless and has been payed attention by…
The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental model-theoretic notion of type.
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
We provide a co-free construction which adds elementary structure to a primary doctrine. We show that the construction preserves comprehensions and all the logical operations which are in the starting doctrine, in the sense that it maps a…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g.,…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed, using an abstract…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…