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Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…
Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the…
In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
We show that provability in the implicational fragment of relevance logic is complete for doubly exponential time, using reductions to and from coverability in branching vector addition systems.
We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional…
Team Semantics generalizes Tarski's Semantics for First Order Logic by allowing formulas to be satisfied or not satisfied by sets of assignments rather than by single assignments. Because of this, in Team Semantics it is possible to extend…
We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
There are now many theoretical explanations for why Benford's law of digit bias surfaces in so many diverse fields and data sets. After briefly reviewing some of these, we discuss in depth recurrence relations. As these are discrete…
It is known that not only classical semantics but also intuitionistic Kripke semantics can be generalized so that it can treat arbitrary propositional connectives characterized by truth tables, or truth functions. In our previous work, it…
We study the relation between additivity and deduction theorems in the algebraic semantics of congruential modal logic. Additivity of the modal operator is well-known to imply the local deduction-detachment theorem. Our main theme is that…
Guarded Interaction Trees are a structure and a fully formalized framework for representing higher-order computations with higher-order effects in Rocq. We present an extension of Guarded Interaction Trees to support formal reasoning about…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
We present a logical framework for the verification of relational properties in imperative programs. Our work is motivated by relational properties which come from security applications and often require reasoning about formulas with…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
The purpose of this note is to complete the interesting review on quantum contextuality [1] that appeared recently. In particular we will introduce and discuss the ideas of extracontextuality and extravalence, that allow one to relate…