Deduction is the ability to draw necessary conclusions from previous knowledge. Here we propose a novel approach to understanding the neural basis of deduction, which exploits fine-grained inter-participant variability in such tasks. Participants solved deductive problems and were grouped by the behavioral strategies employed, i.e., whether they were sensitive to the logical form of syllogistic...

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic. In the papers concerning quan...

Objects like rewrite rules and strategies are of very general use and interest in computer science. They are especially useful when modeling inference based systems like logical frameworks, theorem provers, constraint solvers, expert systems, transition systems. In order to formalize the concept of rule application, we have designed a calculus of explicit rule application called the rewritingor...

One of the main ideas of calculi of natural deduction, as introduced by Jaskowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions which can be discharged. The resulting calculi and derivations with rules of any finite level are in...

Spatial logics are used to reason locally about disjoint data structures. They consist of standard first-order logic constructs, spatial (structural) connectives and their corresponding adjuncts. Lozes has shown that the adjuncts add no expressive power to a spatial logic for analysing tree structures, a surprising and important result. He also showed that a related logic does not have this adj...

We propose a combinatory reformulation of the product free version of the categorial calculus LL, i.e. the associative Lambek calculus that admits empty premises. We prove equivalence of the combinatory with the standard Natural Deduction presentation of LL. The result offers a new perspective on the relation between the type logical and the combinatory branch of the Categorial Grammar research...

A logical framework is presented for representing and reasoning about nondeterministic programs that may not terminate. We propose a logic PDL(; ;, ||, d(∗)) which is an extension of dynamic logic such that the program constructors related to demonic operations are introduced in its language. A complete and sound Hilbert-style proof system is given and it is shown that PDL(; ;, ||, d(∗)) is dec...

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction.

We introduce a new method (derived from model theoretic general combination procedures in automated deduction) for proving fusion decidability in modal systems. We apply it to show fusion decidability in case not only the boolean connectives, but also a universal modality and nominals are shared symbols.

Many modern business environments employ software to automate the delivery of workflows; whereas, workflow design and generation remains a laborious technical task for domain specialists. Several different approaches have been proposed for deriving workflow models. Some approaches rely on process data mining approaches, whereas others have proposed derivations of workflow models from operationa...