Related papers: On Empirical Equivalence and Duality

Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…

The automatic ranking of word pairs as per their semantic relatedness and ability to mimic human notions of semantic relatedness has widespread applications. Measures that rely on raw data (distributional measures) and those that use…

Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…

We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…

A dual action is obtained for a general non-abelian and non-supersymmetric gauge theory at the classical level. The construction follows steps similar to those used in pure abelian gauge theory. As an example we study the spontaneously…

We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…

Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…

A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…

Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…

This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…

We formulate the problem of perception in the framework of information theory, and prove that categorical perception is equivalent to the existence of an observable that has the maximum possible information on the target of perception. We…

A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a…

Dualities offer new possibilities for relating fundamentality and emergence. In particular, as is the aim of this chapter to show, it may happen that the relations of fundamentality and emergence between dual theories are inverted. In other…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued fields. As an application we prove many-one reductions…