This paper is an exercise in formal and philosophical logic. I will show how intuitionistic propositional logic can be extended with a new two-place connective, not expressible in the traditional language of intuitionistic logic (the language of conjunction, disjunction, negation and implication). The new system will be shown to be a conservative extension of intuitionistic logic. After examini...

Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason [12], logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no s...

In recent years, AI research has started to take seriously the role of context in developing models. This trend is heralded by a departure from logic-based views and their over-emphasis on the formal aspects of thought processes. The departure, however, has not been complete| some fundamental assumptions of formal logic are still maintained in the new approaches. Similarly, \relevance" remains ...

In this paper, we discuss formal reconstructions of Anselm’s ontological argument. We first present a number of requirements that any successful reconstruction should meet. We then offer a detailed preparatory study of the basic concepts involved in Anselm’s argument. Next, we present our own reconstructions—one in modal logic and one in classical logic—and compare them with each other and with...

We present a formal specification language and a formal verification logic for a simple object-oriented programming language. The language is applicative and statically typed, and supports subtyping and messagepassing. The verification logic relies on a behavioral notion of subtyping that captures the intuition that a subtype behaves like its supertypes. We give a formal definition for legal su...

We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation’s characterization of a hierarchy of pseudovarieties of finite lattices, progressively generalizing finite distributive lattices. This formal connection is mediated through monotone modal logic. Indeed, we adapt the correspondence algorithm ...

The logic underlying our current interpretations of all first-order formal languages—which provide the formal foundations for all computing languages—is Aristotle’s logic of predicates. I review Rosser’s claim that Gödel’s reasoning can be recast to arrive at his intended result without the assumption of ω-consistency, since Rosser’s argument appeals to a fundamental tenet of this logic, namely...

One of the major roles of logic in computer science and A.I. is for knowledge representation and specification. In the context of knowledge representation, formal logic is widely praised as the tool par excellence for expressing information in a precise way and for correct and precise communication of information between different experts. In the scenario of communicating experts, the experts e...

The logic underlying our current interpretations of all first-order formal languages—which provide the formal foundations for all computing languages—is Aristotle’s logic of predicates. I show, first, that a fundamental tenet of this logic, namely Aristotlean particularisation, is a subjective, and objectively unverifiable, postulation that is ‘stronger’ than the Axiom of Choice; and that, seco...

ABC is a public-domain system for logic synthesis and formal verification of binary logic circuits appearing in synchronous hardware designs. ABC combines scalable logic transformations based on And-Inverter Graphs (AIGs), with a variety of innovative algorithms. A focus on the synergy of sequential synthesis and sequential verification leads to improvements in both domains. This paper introduc...