Related papers: An infinitary model of linear logic

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…

This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stages, is identical to the unique equilibrium of an unbounded…

We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…

This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the…

This paper demonstrates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger…

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…

Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

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…

Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information…

Fitch-style modal deduction, in which modalities are eliminated by opening a subordinate proof, and introduced by shutting one, were investigated in the 1990s as a basis for lambda calculi. We show that such calculi have good computational…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…

The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…

Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be…

This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated…

We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…

Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main…

We are interested in proving input-output properties of functions that handle infinite data such as streams or non-wellfounded trees. We provide a finitary refinement type system which is (sound and) complete for Scott-open properties…