Related papers: On a paraconsistentization functor in the category…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
We present three syntactic forcing models for coherent logic. These are based on sites whose underlying category only depends on the signature of the coherent theory, and they do not presuppose that the logic has equality. As an application…
We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension,…
We derive an analogue of the quantum total probability rule by constructing a probability theory based on paraconsistent logic. Bayesian probability theory is constructed upon classical logic and a desiderata, that is, a set of desired…
The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that first-order logic cannot model interactive…
While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from…
In this article we reconstruct the Frauchiger and Renner argument, taking into account that the assertions of the argument are made at different times. To do this, we use a formalism of quantum histories, namely the Theory of Consistent…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It…