The core of this paper is Chagrova's Theorems about first-order definability of given modal formu... more The core of this paper is Chagrova's Theorems about first-order definability of given modal formulas and modal definability of given elementary conditions. We consider classes of frames for which modal definability is decidable and classes of frames for which first-order definability is trivial. We give a new proof of Chagrova's Theorem about modal definability and sketches of proofs of new variants of Chagrova's Theorem about modal definability.
We present a new general and language independent approach to the noisy text correction problem d... more We present a new general and language independent approach to the noisy text correction problem developed and implemented in the framework of the CULTURA project. We briefly describe the core candidate generator, REBELS, the complete system concept, its efficient implementation based on functional automata and its immediate applications. The quality of the whole system is empirically established in different experimental settings where language and noise sources are varied.
Recent Advances in Natural Language Processing, Sep 1, 2009
The paper presents the results of a project completed by the authors for realizing a continuous s... more The paper presents the results of a project completed by the authors for realizing a continuous speech recognition system for Bulgarian. The state-of-the-art speech recognition technology used in the system is discussed. Special attention is given to the problems with some specics of the Bulgarian language namely the large vocabulary (450000 wordforms). Some implementation details of the language module are given. At the end the paper provides evaluation of the accuracy of recognition.
The core of our article is the computability of the problem of deciding the modal definability of... more The core of our article is the computability of the problem of deciding the modal definability of first-order sentences with respect to classes of frames. It gives a new proof of Chagrova's Theorem telling that, with respect to the class of all frames, the problem of deciding the modal definability of first-order sentences is undecidable. It also gives the proofs of new variants of Chagrova's Theorem.
... Lemma 12. Let φ be a sentence from L(R,=) with quantifier depth k and modally definable by a ... more ... Lemma 12. Let φ be a sentence from L(R,=) with quantifier depth k and modally definable by a δ-formula. ... Now by we denote the partition with equivalence classes each of them with the size 2. The partitions and are k-elementary equivalent by Proposition 2 and therefore.
A. Tarski uses in his system for the elementary geometry only the primitive concept of point, and... more A. Tarski uses in his system for the elementary geometry only the primitive concept of point, and the two primitive relations betweenness and equidistance. Another approach is the relations to be on lines instead of points. W. Schwabhäuser and L. Szczerba showed that perpendicularity together with the ternary relation of co-punctuality are sufficient for dimension two, i.e. they may be used as a system of primitive relations for elementary plane Euclidean geometry. In this paper we give a complete axiomatization for the fragment of elementary plane Euclidean geometry based on perpendicularity alone. We show that this theory is not finitely axiomatizable, it is decidable and the complexity is PSPACE-complete. In contrast the complexity of elementary plane Euclidean geometry is exponential.
We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are i... more We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper we prove that this relation is indeed a contact relation between polytopes, which turns out not to be the case for arbitrary regular closed in Euclidean spaces sets. In the second half we study the universal fragments of the logics of the resultant contact algebras. We prove that they all coincide with the set of theorems of a standard quantifier-free formal system for connected contact algebras, which also coincides with the universal fragments of the logics of a variety of (classes of) contact algebras of interest.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 5, 2014
P RSP DL is a variant of P DL with parallel composition. In the Kripke models in which P RSP DL-f... more P RSP DL is a variant of P DL with parallel composition. In the Kripke models in which P RSP DL-formulas are evaluated, states have an internal structure. We devote this paper to the definability issue of several classes of frames by means of the language of P RSP DL and to the computability issue of P RSP DL-validity for various fragments of the P RSP DL-language and for various classes of P RSP DL-frames.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 30, 2016
Alt1 is the least modal logic containing the formula ✸x → ✷x. It is determined by the class of al... more Alt1 is the least modal logic containing the formula ✸x → ✷x. It is determined by the class of all deterministic frames. The unification problem in Alt1 is to determine, given a formula φ(x1,. .. , xα), whether there exists formulas ψ1,. .. , ψα such that φ(ψ1,. .. , ψα) is in Alt1. In this paper, we show that the unification problem in Alt1 is in P SP ACE. We also show that there exists an Alt1-unifiable formula that has no minimal complete set of unifiers. Finally, we study sub-Boolean variants of the unification problem in Alt1.
ABSTRACT In this paper we investigate several extensions of the first order-language with finitel... more ABSTRACT In this paper we investigate several extensions of the first order-language with finitely many binary relations. The most interesting of the studied extensions appears to be the monadic second-order one. We show that the extended languages have the same expressive power as the first-order language over the class of all relational structures of equivalence relations in local agreement by providing appropriate translation of formulae. The decidability of the considered extensions over the above mentioned class of structures is also shown.
The core of this paper is Chagrova's Theorems about first-order definability of given modal formu... more The core of this paper is Chagrova's Theorems about first-order definability of given modal formulas and modal definability of given elementary conditions. We consider classes of frames for which modal definability is decidable and classes of frames for which first-order definability is trivial. We give a new proof of Chagrova's Theorem about modal definability and sketches of proofs of new variants of Chagrova's Theorem about modal definability.
We prove that modal definability with respect to the class of all structures with two commuting e... more We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The construction used in the proof shows that the same is true for the subclass of all finite structures. For that reason we prove that the first-order theories of these classes are undecidable and reduce the latter problem to the former.
This paper presents a brief description of the semantic relations included in the Bulgarian wordn... more This paper presents a brief description of the semantic relations included in the Bulgarian wordnet. A complete and decidable formal logic for the wordnet structure is also proposed. This logic provides sufficient expressive power for all important verifications, queries, and consistency and completeness proofs required for wordnet applications. Some parameters concerning Bulgarian synsets and language-internal relations, as well as the distinctive features characterizing the completeness and consistency of the Bulgarian wordnet are
It is already known that unifiable formulas in normal modal logic $\textbf {K}+\square ^{2}\bot $... more It is already known that unifiable formulas in normal modal logic $\textbf {K}+\square ^{2}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{2}\bot $ are unitary. In this paper, we prove that for all $d{\geq }3$, unifiable formulas in normal modal logic $\textbf {K}+\square ^{d}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{d}\bot $ are unitary.
PRSPDL is a variant of PDL with parallel composition. In the Kripke models in which PRSPDL-formul... more PRSPDL is a variant of PDL with parallel composition. In the Kripke models in which PRSPDL-formulas are evaluated, states have an internal structure. We devote this paper to the definability issue of several classes of frames by means of the language of PRSPDL and to the computability issue of PRSPDL-validity for various fragments of the PRSPDL-language and for various classes of PRSPDL-frames.
In this paper, we show that every KD45-unifiable formula has a projective unifier. As a corollary... more In this paper, we show that every KD45-unifiable formula has a projective unifier. As a corollary, we conclude that KD45 has unitary type for elementary unification.
This paper is devoted to exploring modal definability of firstorder sentences and first-order def... more This paper is devoted to exploring modal definability of firstorder sentences and first-order definability of modal formulas. It investigates the decidability and the complexity of these problems within the class of all partitions.
The core of this paper is Chagrova's Theorems about first-order definability of given modal formu... more The core of this paper is Chagrova's Theorems about first-order definability of given modal formulas and modal definability of given elementary conditions. We consider classes of frames for which modal definability is decidable and classes of frames for which first-order definability is trivial. We give a new proof of Chagrova's Theorem about modal definability and sketches of proofs of new variants of Chagrova's Theorem about modal definability.
We present a new general and language independent approach to the noisy text correction problem d... more We present a new general and language independent approach to the noisy text correction problem developed and implemented in the framework of the CULTURA project. We briefly describe the core candidate generator, REBELS, the complete system concept, its efficient implementation based on functional automata and its immediate applications. The quality of the whole system is empirically established in different experimental settings where language and noise sources are varied.
Recent Advances in Natural Language Processing, Sep 1, 2009
The paper presents the results of a project completed by the authors for realizing a continuous s... more The paper presents the results of a project completed by the authors for realizing a continuous speech recognition system for Bulgarian. The state-of-the-art speech recognition technology used in the system is discussed. Special attention is given to the problems with some specics of the Bulgarian language namely the large vocabulary (450000 wordforms). Some implementation details of the language module are given. At the end the paper provides evaluation of the accuracy of recognition.
The core of our article is the computability of the problem of deciding the modal definability of... more The core of our article is the computability of the problem of deciding the modal definability of first-order sentences with respect to classes of frames. It gives a new proof of Chagrova's Theorem telling that, with respect to the class of all frames, the problem of deciding the modal definability of first-order sentences is undecidable. It also gives the proofs of new variants of Chagrova's Theorem.
... Lemma 12. Let φ be a sentence from L(R,=) with quantifier depth k and modally definable by a ... more ... Lemma 12. Let φ be a sentence from L(R,=) with quantifier depth k and modally definable by a δ-formula. ... Now by we denote the partition with equivalence classes each of them with the size 2. The partitions and are k-elementary equivalent by Proposition 2 and therefore.
A. Tarski uses in his system for the elementary geometry only the primitive concept of point, and... more A. Tarski uses in his system for the elementary geometry only the primitive concept of point, and the two primitive relations betweenness and equidistance. Another approach is the relations to be on lines instead of points. W. Schwabhäuser and L. Szczerba showed that perpendicularity together with the ternary relation of co-punctuality are sufficient for dimension two, i.e. they may be used as a system of primitive relations for elementary plane Euclidean geometry. In this paper we give a complete axiomatization for the fragment of elementary plane Euclidean geometry based on perpendicularity alone. We show that this theory is not finitely axiomatizable, it is decidable and the complexity is PSPACE-complete. In contrast the complexity of elementary plane Euclidean geometry is exponential.
We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are i... more We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper we prove that this relation is indeed a contact relation between polytopes, which turns out not to be the case for arbitrary regular closed in Euclidean spaces sets. In the second half we study the universal fragments of the logics of the resultant contact algebras. We prove that they all coincide with the set of theorems of a standard quantifier-free formal system for connected contact algebras, which also coincides with the universal fragments of the logics of a variety of (classes of) contact algebras of interest.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 5, 2014
P RSP DL is a variant of P DL with parallel composition. In the Kripke models in which P RSP DL-f... more P RSP DL is a variant of P DL with parallel composition. In the Kripke models in which P RSP DL-formulas are evaluated, states have an internal structure. We devote this paper to the definability issue of several classes of frames by means of the language of P RSP DL and to the computability issue of P RSP DL-validity for various fragments of the P RSP DL-language and for various classes of P RSP DL-frames.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 30, 2016
Alt1 is the least modal logic containing the formula ✸x → ✷x. It is determined by the class of al... more Alt1 is the least modal logic containing the formula ✸x → ✷x. It is determined by the class of all deterministic frames. The unification problem in Alt1 is to determine, given a formula φ(x1,. .. , xα), whether there exists formulas ψ1,. .. , ψα such that φ(ψ1,. .. , ψα) is in Alt1. In this paper, we show that the unification problem in Alt1 is in P SP ACE. We also show that there exists an Alt1-unifiable formula that has no minimal complete set of unifiers. Finally, we study sub-Boolean variants of the unification problem in Alt1.
ABSTRACT In this paper we investigate several extensions of the first order-language with finitel... more ABSTRACT In this paper we investigate several extensions of the first order-language with finitely many binary relations. The most interesting of the studied extensions appears to be the monadic second-order one. We show that the extended languages have the same expressive power as the first-order language over the class of all relational structures of equivalence relations in local agreement by providing appropriate translation of formulae. The decidability of the considered extensions over the above mentioned class of structures is also shown.
The core of this paper is Chagrova's Theorems about first-order definability of given modal formu... more The core of this paper is Chagrova's Theorems about first-order definability of given modal formulas and modal definability of given elementary conditions. We consider classes of frames for which modal definability is decidable and classes of frames for which first-order definability is trivial. We give a new proof of Chagrova's Theorem about modal definability and sketches of proofs of new variants of Chagrova's Theorem about modal definability.
We prove that modal definability with respect to the class of all structures with two commuting e... more We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The construction used in the proof shows that the same is true for the subclass of all finite structures. For that reason we prove that the first-order theories of these classes are undecidable and reduce the latter problem to the former.
This paper presents a brief description of the semantic relations included in the Bulgarian wordn... more This paper presents a brief description of the semantic relations included in the Bulgarian wordnet. A complete and decidable formal logic for the wordnet structure is also proposed. This logic provides sufficient expressive power for all important verifications, queries, and consistency and completeness proofs required for wordnet applications. Some parameters concerning Bulgarian synsets and language-internal relations, as well as the distinctive features characterizing the completeness and consistency of the Bulgarian wordnet are
It is already known that unifiable formulas in normal modal logic $\textbf {K}+\square ^{2}\bot $... more It is already known that unifiable formulas in normal modal logic $\textbf {K}+\square ^{2}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{2}\bot $ are unitary. In this paper, we prove that for all $d{\geq }3$, unifiable formulas in normal modal logic $\textbf {K}+\square ^{d}\bot $ are either finitary or unitary and unifiable formulas in normal modal logic $\textbf {Alt}_{1}+\square ^{d}\bot $ are unitary.
PRSPDL is a variant of PDL with parallel composition. In the Kripke models in which PRSPDL-formul... more PRSPDL is a variant of PDL with parallel composition. In the Kripke models in which PRSPDL-formulas are evaluated, states have an internal structure. We devote this paper to the definability issue of several classes of frames by means of the language of PRSPDL and to the computability issue of PRSPDL-validity for various fragments of the PRSPDL-language and for various classes of PRSPDL-frames.
In this paper, we show that every KD45-unifiable formula has a projective unifier. As a corollary... more In this paper, we show that every KD45-unifiable formula has a projective unifier. As a corollary, we conclude that KD45 has unitary type for elementary unification.
This paper is devoted to exploring modal definability of firstorder sentences and first-order def... more This paper is devoted to exploring modal definability of firstorder sentences and first-order definability of modal formulas. It investigates the decidability and the complexity of these problems within the class of all partitions.
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