Related papers: Elementary Logic in Linear Space

Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…

We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a…

A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…

The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…

Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…

With recent sensor and tracking technology advances, the volume of available trajectory data is steadily increasing. Consequently, managing and analyzing trajectory data has seen significant interest from the research community. The…

In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.

We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…

The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…

In our previous research, we provided a reasoning system (called LeSAC) based on argumentation theory to provide legal support to designers during the design process. Building on this, this paper explores how to provide designers with…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…

We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…