Related papers: Infinitary Logic Has No Expressive Efficiency Over…

Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…

This paper establishes model-theoretic properties of $\mathrm{FOE}^{\infty}$, a variation of monadic first-order logic that features the generalised quantifier $\exists^\infty$ (`there are infinitely many'). We provide syntactically defined…

We define a new class of infinitary logics $\mathscr L^1_{\kappa,\alpha}$ generalizing Shelah's logic $\mathbb L^1_\kappa$ defined in \cite{MR2869022}. If $\kappa=\beth_\kappa$ and $\alpha <\kappa$ is infinite then our logic coincides with…

The Feferman-Vaught theorem provides a way of evaluating a first order sentence $\varphi$ on a disjoint union of structures by producing a decomposition of $\varphi$ into sentences which can be evaluated on the individual structures and the…

Many tasks in statistical and causal inference can be construed as problems of \emph{entailment} in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for \emph{causal}…

We in this paper show that omega regular languages are not closed under infinite union and intersection. As an attempt, we propose to add step variables and quantifiers to temporal logics to enhance the expressiveness of the underlying…

Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…

Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…

Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$ (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite…

We study two extensions of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, "the letter $a$ appears between…

Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of…

We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be…

Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered…

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…

Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…

We firstly show that the standard interpretation of natural quantification in mathematical logic does not provide a satisfying account of its original richness. In particular, it ignores the difference between generic and distributive…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…