Related papers: Multiplicative logic in arithmetic
We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit…
Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored.…
We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field. Describe explicitly the multiple polylogarithm Hopf…
We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination in multiplicative proof nets corresponds to instances of…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
We define a Hopf algebra of polylogarithms of an arbitrary field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and mimics Goncharov's construction of higher Bloch groups. We…
We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a…
We calculate the formal analytic expansions of certain formal translations in a space of formal iterated logarithmic and exponential variables. The results show how the algebraic structure naturally involves the Stirling numbers of the…
A classical logic exhibits a threefold inner structure comprising an algebra of propositions `A', a space of ``truth values'' `V', and a distinguished family of mappings `phi' from propositions to truth values. Classically A is a Boolean…
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a…
Combining predictions from different models is a central problem in Bayesian inference and machine learning more broadly. Currently, these predictive distributions are almost exclusively combined using linear mixtures such as Bayesian model…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal…