Related papers: Saturation properties for compositional truth with…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
The material conditional has long been charged with paradox. Defined truth-functionally, it renders true any conditional whose antecedent is false or consequent true -- hence, seemingly absurd statements such as `If unicorns exist, then…
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental…
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Compositionality has traditionally been understood as a major factor in productivity of language and, more broadly, human cognition. Yet, recently, some research started to question its status, showing that artificial neural networks are…
In this paper, we focus on discrete-time stochastic systems modelled by nonlinear stochastic difference equations and propose robust abstractions for verifying probabilistic linear temporal specifications. The current literature focuses on…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
We define a notion of model for the $\lambda$$\Pi$-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the $\lambda$$\Pi$-calculus modulo any…
Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general,…
A theory $T$ is said to have exact saturation at a singular cardinal $\kappa$ if it has a $\kappa$-saturated model which is not $\kappa^{+}$-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language…
Coherent information is a useful concept in quantum information theory. It connects with other notions in data processing. In this short remark, we discuss the coherent information saturating its upper bound. A necessary and sufficient…
In this paper we split every basic propositional connective into two versions, one is called extensional and the other one intensional. The extensional connectives are semantically characterized by standard truth conditions that are…
Program semantics can often be expressed as a (many-sorted) first-order theory S, and program properties as sentences $\varphi$ which are intended to hold in the canonical model of such a theory, which is often incomputable. Recently, we…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
Bisimulation metric is a robust behavioural semantics for probabilistic processes. Given any SOS specification of probabilistic processes, we provide a method to compute for each operator of the language its respective metric…
In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…