Related papers: An infinitary model of linear logic
Given a structure $M$ we introduce infinitary logic expansions, which generalise the Morleyisation. We show that these expansions are tame, in the sense that they preserve and reflect both the Embedding Ramsey Property (ERP) and the…
Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for…
In this paper, we have described a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted by bounded…
This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence…
I study the modal theory of linear orders under embeddings, monotone maps, condensations, and end-extensions. I prove modality elimination for embeddings and monotone maps, show that condensations make scatteredness modally definable, and…
We prove several representation theorems for infinitary predicate modal logic
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation…
The aim of this of this paper is to study infinite games and to prove formally some properties in this framework. As a consequence we show that the behavior (the madness) of people which leads to speculative crashes or escalation can be…
In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…
The paper introduces a basic logic of knowledge and abduction by extending Levesque logic of only-knowing with an abduction modal operator defined via the combination of basic epistemic concepts. The upshot is an alternative approach to…
We present infinite extensive strategy profiles with perfect information and we show that replacing finite by infinite changes the notions and the reasoning tools. The presentation uses a formalism recently developed by logicians and…
We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited…
Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of…