Keehang Kwon

Keehang Kwon

We present a novel definition of an algorithm and its corresponding algorithm language called CoLweb. The merit of CoLweb [1] is that it makes algorithm design so versatile. That is, it forces us to a high-level, proof-carrying, distributed-style approach to algorithm design for both non-distributed computing and distributed one. We argue that this approach simplifies algorithm design. In addition, it unifies other approaches including recursive logical/functional algorithms, imperative algorithms, object-oriented imperative algorithms, neural-nets, interaction nets, proof-carrying code, etc. As an application, we refine Horn clause definitions into two kinds: blind-univerally-quantified (BUQ) ones and parallel-universally-quantified (PUQ) ones. BUQ definitions corresponds to the traditional ones such as those in Prolog where knowledgebase is $not$ expanding and its proof procedure is based on the backward chaining. On the other hand, in PUQ definitions, knowledgebase is $expanding$ and its proof procedure leads to forward chaining and {\it automatic memoization}.

Keehang Kwon

{\em Computability logic} (CoL) is a powerful, mathematically rigorous computational model. In this paper, we show that CoL-web, a web extension to CoL, naturally supports web programming where database updates are involved. To be specific, we discuss an implementation of the AI ATM based on CoL (CL9 to be exact). More importantly, we argue that CoL-web supports a general AI and, therefore, is a good alternative to neural nets and deep learning. We also discuss how to integrate neural nets into CoL-web.

Keehang Kwon

Computability logic(CoL) is a powerful computational model. In this paper, we show that CoL naturally supports multi-agent programming models where resources (coffee for example) are involved. To be specific, we discuss an implementation of the Starbucks based on CoL (CL2 to be exact).

Keehang Kwon, Daeseong Kang

We discuss an agent-based approach to proof design and implementation, which we call {\it Lemma Flow Diagram} (LFD). This approach is based on the multicut rule with $shared$ cuts. This approach is modular and easy to use, read and automate. Thus, we consider LFD an appealing alternative to `flow proof' which is popular in mathematical education. Some examples are provided.

Keehang Kwon

{\em Computability logic} (CoL) is a powerful computational model which views computational problems as games played by a machine and its environment. In this paper, we show that CoL naturally supports multiagent programming models with distributed control. To be specific, we discuss a distributed logic programming model based on CoL (CL1 to be exact), which we call CL1^Ω. The key feature of this model is that it supports $dynamic/evolving$ knowledgebase of an agent. This model turns out to be a promising approach to reaching both general AI and future computing model.

Keehang Kwon

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which is central to probability theory. The probability theory based on CoL is therefore useful for {\it automating} uncertainty reasoning. We describe some basic properties of this new probability theory. We also discuss a novel isomorphism between the set operations and computability logic operations.

Keehang Kwon, Mi-Young Park

Knowledge Representation (KR) is traditionally based on the logic of facts, expressed in boolean logic. However, facts about an agent can also be seen as a set of accomplished tasks by the agent. This paper proposes a new approach to KR: the notion of task logical KR based on Computability Logic. This notion allows the user to represent both accomplished tasks and accomplishable tasks by the agent. This notion allows us to build sophisticated KRs about many interesting agents, which have not been supported by previous logical languages.