The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well deened formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides ba...

In a recent paper, Ginsberg shows how a backward-chaining ATMS can be used to construct a theorem prover for circumscription. Here, this work is extended to handle prioritized circumscription. The ideas to be described have been implemented, and examples are given of the system in use. 1 Introduction Of all the approaches to nonmonotonic reasoning, Mc-Carthy's circumscription [McCarthy, 1980, M...

When people write a report that involves a complex argument towards a conclusion, they can use a design tool called the inference tree, which enables them to outline the argument, and quickly detect reasoning errors in the outline. Yet when the argument is very complex, the inference tree may spread over several pages, so that writers may often have to flip back and forth between those pages. T...

Graphplan has attracted considerable interest because of its extremely high performance, but the algorithm’s inability to handle action representations more expressive than STRIPS is a major limitation. In particular, extending Graphplan to handle conditional effects is a surprisingly subtle enterprise. In this paper, we describe the space of possible alternatives, and then concentrate on one p...

McIlraith & Allin, CSC384, University of Toronto, Winter 2018 Knowledge Representation (KR) • This material is covered in chapters 7– 9 and 12 (R&N, 3rd ed) (chapters 7—10 (R&N, 2nd ed) ). • Chapter 7 provides useful motivation for logic, and an introduction to some basic ideas. It also introduces propositional logic, which is a good background for first-order logic. • What we cover here is mai...

Most of today's terminological representation systems implement hybrid reasoning architectures wherein a concept classiier is employed to reason about concept deenitions, and a separate recog-nizer is invoked to compute instantiation relations between concepts and instances. Whereas most of the existing recognizer algorithms designed to maximally exploit the reasoning supplied by the concept cl...

We develop various proof techniques for the synthesis of sorting algorithms on binary trees, by extending our previous work on the synthesis of algorithms on lists. Appropriate induction principles are designed and various speci c prove-solve methods are experimented, mixing rewriting with assumption-based forward reasoning and goal-based backward reasoning à la Prolog. The proof techniques are...

State estimation is the task of estimating the state of a partially observable dynamical system given a sequence of executed actions and observations. In logical settings, state estimation can be realized via logical filtering. Unfortunately such filtering, though exact, can be intractable. To this end, we propose logical smoothing, a form of backwards reasoning that works in concert with logic...

We present the theory and implementation of a theorem prover for first-order intuitionistic linear logic based on the inverse method. The central proof-theoretic insights underlying the prover concern resource management and focused derivations, both of which are traditionally understood in the domain of backward reasoning systems such as logic programming. We illustrate how resource management...

A hypothetical reasoning system & an important framework in the development of advanced knowledge-based systems. It can be effectively applied to many practical problems including model-based diagnosis, and designs. However, the inference speed of its PROLOG-based implementation is slow, and this is particularly because of inefficient backtracking. In order to overcome this problem, a fast hypo...