Related papers: Reflections on existential types
We present a method for determining the one-dimensional submodules of a Laurent-Ore module. The method is based on a correspondence between hyperexponential solutions of associated systems and one-dimensional submodules. The…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Reflective systems allow their own structures to be altered from within. Here we are concerned with a style of reflection, called linguistic reflection, which is the ability of a running program to generate new program fragments and to…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
Session-types specify communication protocols for communicating processes, and session-typed languages are often specified using substructural operational semantics given by multiset rewriting systems. We give an observed communication…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
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…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
Causal-consistent reversibility is the reference notion of reversibility for concurrency. We introduce a modular framework for defining causal-consistent reversible extensions of concurrent models and languages. We show how our framework…
The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…
Given a class $\mathcal C$ of models, a binary relation ${\mathcal R}$ between models, and a model-theoretic language $L$, we consider the modal logic and the modal algebra of the theory of $\mathcal C$ in $L$ where the modal operator is…
We establish a close connection between a reversible programming language based on type isomorphisms and a formally presented univalent universe. The correspondence relates combinators witnessing type isomorphisms in the programming…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…