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BDI logic is widely used to describe agent based systems, since it can express a lot of different real world domains with three main operators: belief, desire and intention. There are lots of works where BDI logic is used as descriptive language, but authors do not talk about implementation issues [5,2,4,8,1]. There is even known general agent implementation scheme, which do not describe howto use formal logic for such scheme implementation [12]. The main aim of this paper is to show the bridge, which connects formal and practical parts of logic. We describe how sequent calculus can be used for implementing some parts of general scheme. In this paper, we show how flexible constraints can be implemented. Sequent calculus usage is illustrated with simple examples.

Brodsky’s coding method for propositional logic is considered in the paper. Based on the sequent calculus, the method allows us to determine whether an arbitrary sequent is derivable in the calculus without constructing proof-search trees. The coding method, presented in the paper, can be used as a decision procedure for propositional logic.

In the paper a method to check termination of history-free proof for linear modal logic S4.3 is proposed. This method improves the method proposed by the authors for modal logic S4. Analogously as for S4, instead of history we use marks and indices that allow us to eliminate loop checking. The method proposed in this paper specifies some kind of formulas which allow us to check termination of derivations in more effective way in comparison with S4.

This paper defines decision algorithm for subclass of BKD45DKDIKD logic which is based on known algorithm for temporal BKD45DKDIKD logic [2]. BDI logics are widely used in agent based systems. Such usage of BDI logic can be found in [1]. The original decision algorithm uses loop-check technique for BEL and temporal operators. Applied loop-check technique is not optimized and therefore loop-check takes most of the time used in decision algorithm. Some examples of efficient loop-check applications for logic KT, S4 and some subclasses of intuitionistic logic can be found in [4]. Another efficient loop-check can be found in work [3]. We concentrate on our attitude on loop-check optimization for BEL operator. This paper defines decision algorithm modification, which uses efficient loop-check for BEL operator, but do not effect performance of other parts of algorithm. We define optimization only for BEL operator and therefore we omit temporal operators in this paper.

It is known that traditional techniques used to ensure termination of a decision procedure in non-classical logics are based on loop-checking, in general. Nowadays, effective loop-check techniques based on histories are used instead of unrestricted loop-check. These techniques are widely and successfully applied also for non-classical logics containing induction-like axioms. These induction-like axioms create new type loops (“good loops”) along with ordinary “bad loops”. In this paper, some loop-check free saturation-like decision procedure based on some technique of marks is proposed. This saturation procedure terminates when special type marked sequents are obtained. This procedure is demonstrated for propositional linear temporal logic (PLTL) with temporal operators “next” and “always”.

It is known that one of main aims of specializations of derivations in nonclassical logics is the various tools which allow us to simplify the searching of termination of derivations. The traditional techniques used to ensure termination of derivations in various non-classical logics are based on loop-checking. In this paper the reflexive common knowledge logic based on modal logic K2 is considered. For considered logic a sequent calculus with specialized non-logical (loop-type) axioms is presented.

It is known that termination and backtracking are among the most important problems in constructing derivations in non-classical logics. In this paper contractionfree and backtracking-free sequent calculi for modal logics S5 and KD45 are presented and founded. These are index-style sequent calculi with some specific indexed axioms. The main new ideas in considered calculi are to use metavariables (along with natural numbers) as elements of indexes and to numerate by different natural number all the positive occurrences of modality 2.

In this paper, some loop-check free saturation-like decision procedure is proposed for propositional linear temporal logic (PLTL) with temporal operators “next” and “always”. This saturation procedure terminates when special type sequents are obtained. Properties of PLTL allows us to construct backtracking-free decision procedure without histories and loop-check.

Sound and complete sequent calculi for general epistemic logic and logic of correlated knowledge are presented in this paper.

Hilbert style, Gentzen style sequent and Kanger style sequent calculi for logic S5n(ED) are considered in this paper. Gentzen style sequent calculus is constructed and its equivalence with Hilbert style system is proved, getting soundness and completeness of Gentzen style system. Kanger style indexed sequent calculus is defined for cut elimination.

In the paper loop-check-free sequent calculus for logic of idealized knowledge is presented. To obtain termination of derivation indices and marks are used instead of history.

The paper deals with specialization of the antecedent negation loop-rule for the negative implication free fragment of the propositional intuitionistic logic.

In this paper, we present sequent calculus for branching-time temporal logic with until operator. This sequent calculus uses efficient loop-checktechinque. We prove that we can use not all but only several special sequents from the derivation tree for the loop-check. We use indexes to discover these special sequents in the sequent calculus. These restrictions let us to get efficient decision procedure based on introduced sequent calculus.

It is known that loop checking and backtracking are extensively used in various non-classical logics. An efficient loop checking is obtained using a technique based on histories. In the paper a method for elimination of loop checking in backward proof search for minimal tense logic Kt is proposed. To obtain termination of derivation indices and marks are used instead of history.

In this paper the first order predicate calculus with the axioms of additive arithmetic is investigated. The conditions of the equivalent replaceability of a double induction axiom is presented.

This paper describes a new tactic for proof-search in Hybrid logic H(@), which always terminates.

In this paper, we present sequent calculus for linear temporal logic. This sequent calculus uses efficient loop-check techinque. We prove that we can use not all but only several special sequents from the derivation tree for the loop-check. We use indexes to discover these special sequents in the sequent calculus. These restrictions let us to get efficient decision procedure based on introduced sequent calculus.