Related papers: Characterizing Quantifier Extensions of Dependence…
We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…
We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi$ (in $\mathcal{L}_{\omega,\omega}$) is…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
We propose an extension of Poole's independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This…
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…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Causal multiteam semantics is a framework where probabilistic dependencies arising from data and causation between variables can be together formalized and studied logically. We consider several logics in the setting of causal multiteam…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We study the expressivity and the complexity of various logics in probabilistic team semantics with the Boolean negation. In particular, we study the extension of probabilistic independence logic with the Boolean negation, and a recently…
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 product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…