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Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok…
We report our findings on the properties of Flagg and Friedman's translation from Epistemic into Intuitionistic logic, which was proposed as the basis of a comprehensive proof method for the faithfulness of the Goodel translation. We focus…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
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…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…
The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…
We present the intuitionistic version of PUC-Logic. After that, we present a constructive approach to Lewis' counterfactual abstraction to show that it does not require the classical absurd rule.
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…
Topological semantics for modal logics has recently gained new momentum in many different branches of logic. In this paper, we will consider the topological semantics of both classical and paraconsistent modal logics. This work is a new…
An indeterministic interpretation of classical physics has been proposed recently, in which the argument relies on attacking an alleged unwarranted metaphysical hidden assumption of the standard deterministic interpretation. This short…
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…
One advantage of paraconsistent logic is that it can deal with inconsistencies without making the system trivial. However, unlike classical propositional calculus, its deductive system is limited, and the meaning of paraconsistent negation…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
In this paper I discuss what, according to my long experience, every computer scientist should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
Classical results on aperiodic tilings are rather complicated and not widely understood. Below, an alternative approach is discussed in hope to provide additional intuition not apparent in classical works.
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…