On a logical problem

Plantinga and the Logical Problem of Evil

Logical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem

Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...

Generalizing Problem Reduction: A Logical Analysis

Froblcm reduction is the name given to the problem-solving paradigm in which the problem solver manages a network of "tasks" representing its intentions, repeatedly reducing tasks to subtasks and coordinating their execution. This idea needs a lot of generalization for it to be able to handle a realistic range of problems. Even after the model of time is made more realistic (to handle continuit...

Logical Relations in a Statistical Problem

This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input, and it introduces a common calculus for making inferences in the framework. After an introduction to the programme as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework and c...

Logical Refinements of Church's Problem

Church’s Problem (1962) asks for the construction of a procedure which, given a logical specification φ on sequence pairs, realizes for any input sequence X an output sequence Y such that (X,Y ) satisfies φ. Büchi and Landweber (1969) gave a solution for MSO specifications in terms of finite-state automata. We address the problem in a more general logical setting where not only the specificatio...