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Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
We propose here to look at how abstract a model of a usable system can be, but still say something useful and interesting, so this paper is an exercise in abstraction and formalisation, with usability-of-design as an example target use. We…
Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…
The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…
In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…
A first order inference system, called R-calculus, is defined to develop the specifications. It is used to eliminate the laws which is not consistent with the user's requirements. The R-calculus consists of the structural rules, an axiom, a…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Software and hardware architectures are prone to modifications. We demonstrate how a mathematically founded powerful refinement calculus for a class of architectures, namely pipe and filter architectures, can be used to modify a system in a…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.
Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…
In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…