Related papers: A fundamental non-classical logic
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
It is well-known that intuitionistic logics can be formalized by means of Brouwerian semilattices, i.e. relatively pseudocomplemented semilattices. Then the logical connective implication is considered to be the relative pseudocomplement…
This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: 'What…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…
This report first shows the equivalence bewteen several formulations of classical logic in intuitionistic logic (tertium non datur, reductio ad absurdum, Pierce's law). Then it establishes the correctness of the G\"odel-Kolmogorov…
Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Natural deduction systems, as proposed by Gentzen and further studied by Prawitz, is one of the most well known proof-theoretical frameworks. Part of its success is based on the fact that natural deduction rules present a simple…
In their seminal paper Birkhoff and von Neumann revealed the following dilemma: "... whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…