Related papers: An approximate logic for measures

Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…

Counting the contribution rate of a world-line formula to Feynman diagrams in $\phi^3$ theory, we explain the idea how to determine precise combinatorics of Bern-Kosower-like amplitudes derived from a bosonic string theory for $N$-point…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

Furstenberg and Glasner proved that for an arbitrary k in N, any piecewise syndetic set contains k term arithmetic progression and such collection is also piecewise syndetic in Z. They used algebraic structure of beta N. The above result…

We show that any ergodic measure for a piecewise monotonic map with positive metric entropy is approximated by periodic measures in the weak-* sense. This partially answers Hofbauer-Raith's conjecture.

We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

Given a category C of a combinatorial nature, we study the following fundamental question: how does the combinatorial behavior of C affect the algebraic behavior of representations of C? We prove two general results. The first gives a…

In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…

We provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of \emph{generalized Fej\'er monotonicity} where (1) the metric can be replaced by a much more general type…

The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings,…

Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…

Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…

One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…

We give a short combinatorial proof of the classical pointwise ergodic theorem for probability measure preserving $\mathbb{Z}$-actions. Our approach reduces the theorem to a tiling problem: tightly tile each orbit by intervals with desired…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…