Related papers: Is Peirce's reduction thesis gerrymandered?
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…
We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which…
Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…
The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
Often fairness assumptions need to be made in order to establish liveness properties of distributed systems, but in many situations these lead to false conclusions. This document presents a research agenda aiming at laying the foundations…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances…
Even though query evaluation is a fundamental task in databases, known classifications of conjunctive queries by their fine-grained complexity only apply to queries without self-joins. We study how self-joins affect enumeration complexity,…
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z_3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…
We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree form (in particular, a ternary form) instead of a quadratic…
Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as…
Principles of cognitive economy would require that concepts about objects, properties and relations should be introduced only if they simplify the conceptualisation of a domain. Unexpectedly, classic logic conditionals, specifying…