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Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
Evaluation is a critical activity associated with any theory. Yet this has proven to be an exceptionally challenging activity for theories based on cognitive architectures. For an overlapping set of reasons, evaluation can also be…
The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that…
Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical…
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
The work argues the principle of equivalence to be a theorem and not a principle (in a sense of an axiom). It contains a detailed analysis of the concepts of normal and inertial frame of reference. The equivalence principle is proved to be…
It is known that the theory of any class of normed spaces over the reals that includes all spaces of a given dimension d > 1 is undecidable, and indeed, admits a relative interpretation of second-order arithmetic. The notion of a normed…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
In three papers Colbeck and Renner (Nature Communications 2:411, (2011); Phys. Rev. Lett. 108, 150402 (2012); arXiv:1208.4123) argued that "no alternative theory compatible with quantum theory and satisfying the freedom of choice assumption…
We show that quantum game theory offers solution to the famous Newcomb's paradox (free will problem). Divine foreknowledge is not necessary for successful completion of the game because quantum theory offers a way to discern human…
In my opinion, nothing useful has ever been written on the question in the title, and small is the contribution that I have to offer. I outline an explanation for why there is something rather than nothing, an explanation which, however, I…
Moses & Nachum ([7]) identify conceptual flaws in Bacharach's generalization ([3]) of Aumann's seminal "agreeing to disagree" result ([1]). Essentially, Bacharach's framework requires agents' decision functions to be defined over events…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…