We investigate the logical foundations of contracts in distributed applications. A contract is an agreement stipulated between two or more parties, which speci es the duties and the rights of the parties involved therein. We model contracts as formulae in an intuitionistic logic extended with a contractual form of implication . This supports for a variant of Modus Ponens, where from a promise a...

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ‘If Sally is deceiving, I do not believe it’) and Moore’s Paradox that both claims are wrong. I then develop...

We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand’s False Lemma by Gödel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its conseq...

We present quantitative separation logic (QSL). In contrast to classical separation logic, QSL employs quantities which evaluate to real numbers instead of predicates which evaluate to boolean values. The connectives of classical separation logic, separating conjunction (⋆) and separating implication (−−⋆ ), are both lifted from predicates to quantities. This extension is conservative: Both con...

Consequential conditionals are defined as "if P then Q" statements, where P is an action, and Q a predicted outcome of this action, which is either desirable or undesirable to the agent. Experiment 1 shows that desirable (viz. undesirable) outcomes invite an inference to the truth (viz. falsity) of their antecedent. Experiment 2 shows that the more extreme the outcome is, the stronger the invit...

Boundary logic is a formal diagrammatic system that combines Peirce's Entitative Graphs with Spencer Brown's Laws of Form. Its conceptual basis includes boundary forms composed of non-intersecting closed curves, voidsubstitution (deletion of irrelevant structure) as the primary mechanism of reduction, and spatial pattern-equations that define valid transformations. Pure boundary algebra, free o...

An implication operator A is said to be tied if there is a binary operation T that ties A; that is, the identity A(a,A(b, z)) = A(T (a, b), z) holds for all a, b, z. We aim at the construction of a complete predicate logic for prelinear tied adjointness algebras. We realize this in three steps. In the first step, we establish a propositional calculus AdjTPC, complete for the class of all tied a...

An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inferenc...

Proof: 1.1. Every mef will be of the form p—> p in virtue of variablesharing. Eefs of the form p —> C and C -+ p, where C is an ef, are ruled out, the first because of the Ackermann property, the second because by modus ponens p would be a theorem. So every eef is a mef, and Lemma 1.1. follows. 1.2. Let A contain two or more propositional variables. In virtue of variable-sharing every ef of A c...

Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of finitistic arithmetic. They are tree-like structures, formed metatheory, equations between numerals on which concrete arithmetical sentences evaluated. As first step towards classical formalisation we propose their counterparts...