Related papers: Classical Mathematics for a Constructive World
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
Some instances of creative thinking require an agent to build and test hypothetical theories. Such a reasoner needs to explore the space of not only those situations that have occurred in the past, but also those that are rationally…
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…
We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More…
We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently…
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
"Church's thesis" ($\mathsf{CT}$) as an axiom in constructive logic states that every total function of type $\mathbb{N} \to \mathbb{N}$ is computable, i.e. definable in a model of computation. $\mathsf{CT}$ is inconsistent in both…
We present a new type system with support for proofs of programs in a call-by-value language with control operators. The proof mechanism relies on observational equivalence of (untyped) programs. It appears in two type constructors, which…
This short note presents a new formal language, lambda dependency-based compositional semantics (lambda DCS) for representing logical forms in semantic parsing. By eliminating variables and making existential quantification implicit, lambda…
We investigate different set-theoretic constructions in Residuated Logic based on Fitting's work on Intuitionistic Set Theory. We start by stating some results concerning constructible sets within valued models of Set Theory. We present two…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
How did humanity coax mathematics from the aether? We explore the Platonic view that mathematics can be discovered from its axioms - a game of conjecture and proof. We describe Minimo (Mathematics from Intrinsic Motivation): an agent that…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…