This paper proposes a new approach to defining and expressing algorithms: the notion of task logical algorithms. This notion allows the user to define an algorithm for a task T as a set of agents who can collectively perform T. This notion considerably simplifies the algorithm development process and can be seen as an integration of the sequential pseudocode and logical algorithms. This observation requires some changes to algorithm development process. We propose a two-step approach: the first step is to define an algorithm for a task T via a set of agents that can collectively perform T. The second step is to translate these agents into (higher-order) computability logic.

Adding versatile interactions to imperative programming - C, Java and Android - is an essential task. Unfortunately, existing languages provide only limited constructs for user interaction. These constructs are usually in the form of unbounded quantification. For example, existing languages can take the keyboard input from the user only via the read(x)/scan(x) statement. Note that the value of x is unbounded in the sense that x can have any value. This statement is thus not useful for applications with bounded inputs. To support bounded choices, we propose new bounded-choice statements for user interation. Each input device (keyboard, mouse, touchpad, ...) naturally requires a new bounded-choice statement. To make things simple, however, we focus on a bounded-choice statement for keyboard - kchoose - to allow for more controlled and more guided participation from the user. We illustrate our idea via CBI, an extension of the core C with a new bounded-choice statement for the keyboard.

Inspired by the efficient proof procedures discussed in Computability logic [3],[5],[6], we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system [2] and has the following features: (a) it views sequents as games between the machine and the environment, and (b) it views proofs as a winning strategy of the machine. From this game-based viewpoint, a poweful heuristic can be extracted and a fair degree of determinism in proof search can be obtained. This article proposes a new deductive system LKg with respect to first-order logic and proves its soundness and completeness.

To deal with failures as simply as possible, we propose a new foundation for the core (untyped) C++, which is based on a new logic called task logic or imperative logic. We then introduce a sequential-disjunctive statement of the form S : R. This statement has the following semantics: execute S and R sequentially. It is considered a success if at least one of S, R is a success. This statement is useful for dealing with inessential errors without explicitly catching them.

We propose a query language based on extended regular expressions. This language extends texts with text-generating macros. These macros make it possible to define languages in a compressed, elegant way. This paper also extends queries with linear implications and additive (classical) conjunctions. To be precise, it allows goals of the form D —ο G and G1&G2 where D is a text or a macro and G is a query. The first goal is solved by adding D to the current text and then solving G. This goal is flexible in controlling the current text dynamically. The second goal is solved by solving both G1 and G2 from the current text. This goal is particularly useful for internet search.

We propose HHWeb, an extension to LogicWeb with hereditary Harrop formulas. HHWeb extends the LogicWeb of Loke and Davison by allowing goals of the form ( x1... xn D) G (or equivalently x1... xn(D G)) where D is a web page and G is a goal. This goal is intended to be solved by instantiating x1,...,xn in D by new names and then solving the resulting goal. The existential quantifications at the head of web pages are particularly flexible in controlling the visibility of names. For example, they can provide scope to functions and constants as well as to predicates. In addition, they have such simple semantics that implementation becomes more efficient. Finally, they provide a client-side interface which is useful for customizing web pages.

To represent interactive objects, we propose a choice-disjunctive declaration statement of the form $S add R$ where S, R are the (procedure or field) declaration statements within a class. This statement has the following semantics: request the user to choose one between S and R when an object of this class is created. This statement is useful for representing interactive objects that require interaction with the user.

One of the long-standing research problems on logic programming is to treat the cut predicate in a logical, high-level way. We argue that this problem can be solved by adopting linear logic and choice-disjunctive goal formulas of the form G0 ⊕ G1 where G0, G1 are goals. These goals have the following intended semantics: choose the true disjunct Gi and execute Gi where i (= 0 or 1), while discarding the unchosen disjunct. Note that only one goal can remain alive during execution. These goals thus allow us to specify mutually exclusive tasks in a high-level way. Note that there is another use of cut which is for breaking out of failure-driven loops and efficient heap management. Unfortunately, it is not possible to replace cut of this kind with use of choice-disjunctive goals.