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We study expressibility in infinitary languages of the modal operators associated with satisfiability of sentences of these languages in submodels and extensions of models. We give a syntactic criterion for expressibility in finitary…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(\iota \to \iota) \to \iota$ in the set-theoretical model is a continuous function $(\mathbb{N} \to \mathbb{N}) \to \mathbb{N}$. For…
We use a model of opinion formation to study the consequences of some mechanisms attempting to enforce the right behaviour in a society. We start from a model where the possible choices are not equivalent (such is the case when the agents…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
We present a novel technique for proving program termination which introduces a new dimension of modularity. Existing techniques use the program to incrementally construct a termination proof. While the proof keeps changing, the program…
Formalizing creativity-related concepts has been a long-term goal of Computational Creativity. To the same end, we explore Formal Learning Theory in the context of creativity. We provide an introduction to the main concepts of this…
We extend dynamic logic of propositional assignments by adding an operator of parallel composition that is inspired by separation logics. We provide an axiomatisation via reduction axioms, thereby establishing decidability. We also prove…
We adapt the classical notion of building models by games to the setting of continuous model theory. As an application, we study to what extent canonical operator algebras are enforceable models. For example, we show that the hyperfinite…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
In traditional machine teaching, a teacher wants to teach a concept to a learner, by means of a finite set of examples, the witness set. But concepts can have many equivalent representations. This redundancy strongly affects the search…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Choice and independence of premise principles play an important role in characterizing Kreisel's modified realizability and G\"odel's Dialectica interpretation. In this paper we show that a great many intuitionistic set theories are closed…
We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on $\omega_2$ using finite conditions.
Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated
Complexity of the problem of choosing among uncertain acts is a salient feature of many of the environments in which departures from expected utility theory are observed. I propose and axiomatize a model of choice under uncertainty in which…
In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on…