A |

Abelian groups | Walker's Cancellation Theorem |

admissible rules | A Syntactic Characterization of the Gabbay-de Jongh Logics |

algebraic geometry | A general framework for geometric dualities for varieties of algebras |

algebraic logic | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

algorithmic correspondence | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 1 |

Almost structural completeness | Almost structural completeness; an algebraic approach |

archimedean lattice-ordered group | Truncated Vector Lattices |

B |

basic logic | Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras |

Belnap logic | Four-valued modal logic: Kripke semantics and duality |

bimodule | Fractal Sets as Final Coalgebras Obtained by Completing an Initial Algebra |

BL-algebra | Chang-Mundici construction of an enveloping unital lattice-group of a BL-algebra |

Boolean algebra | A new Glivenko Theorem |

Boolean power | Idempotent generated algebras and Boolean powers of commutative rings |

Boolean-like algebra | Boolean like algebras |

Bull theorem | An analogue of Bull's theorem for Hybrid Logic |

Burnside problem | Residuated Lattices, Regular Languages, and Burnside Problem |

C |

C*-algebra | Open projections do not form a right residuated lattice Effect algebras with state operator |

Canonical Formula | Jankov Formula and Ternary Deductive Term |

Cantor derivative | On the modal logic of the iterated Cantor derivative and finitary operations on topological spaces |

Categorical adjunction | A general framework for geometric dualities for varieties of algebras |

categorical logic | General Topos Semantics for Higher-Order Modal Logic |

Categorical methods in logic | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

categorical proof theory | Cuts for circular proofs |

categorically-algebraic topology | On fuzzification of topological categories |

category theory | Scheme representation for first-order logic |

Cayley | Cayley and Holland Theorems for Residuated Lattices |

closed maps | On the modal logic of the iterated Cantor derivative and finitary operations on topological spaces |

co-algebra | Entropic Hopf algebras |

Co-medial algebra | Representation of the Medial-Like Algebras |

Co-paramedial algebra | Representation of the Medial-Like Algebras |

coalgebra | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

commutative monoid | Entropic Hopf algebras |

compact Hausdorff space | Truncated Vector Lattices Idempotent generated algebras and Boolean powers of commutative rings |

completely separated sublocales | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

conditional expectation | Effect algebras with state operator |

constant domains principle | On the constant domains principle and its weakened versions in the Kripke sheaf semantics |

Constructivism | Walker's Cancellation Theorem |

continuous extension | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

Continuous poset | Dcpo models of T<sub>1</sub> spaces |

continuous real function | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

continuous real-valued function | Truncated Vector Lattices |

conucleus | Reducts and Modal Operators on Residuated Lattices |

convex effect algebra | Effect algebras with state operator |

correspondence theory | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2 |

countable model property | Topological completeness of extensions of S4 |

D |

dcpo | Dcpo models of T<sub>1</sub> spaces |

De Morgan monoids | Relevant logic and relation algebras |

decision procedure | Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras |

derivatinal operator | Derivational modal logic of real line with difference modality |

derivational modal logic | On the modal logic of the iterated Cantor derivative and finitary operations on topological spaces |

Di Nolas representation Theorem | An elementary proof of the completeness of the Lukasiewicz axioms |

diagram category | Walker's Cancellation Theorem |

difference modality | Derivational modal logic of real line with difference modality |

discriminator variety | Boolean like algebras |

double-pointed variety | Boolean like algebras |

E |

effect algebra | Extensions of ordering sets of states from effect algebras onto their MacNeille completions Effect algebras, witness pairs and observables On (finite) distributive lattices with antitone involutions Effect algebras with state operator |

Entropic Algebra | Entropic Hopf algebras |

equationally definable principal relative congruences | Almost structural completeness; an algebraic approach |

Esakia duality | Priestley duality for (modal) N4-lattices |

Extended-order algebras | Relational groupoids and residuated lattices |

extremally disconnected frame | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

F |

Farkas' Lemma | An elementary proof of the completeness of the Lukasiewicz axioms |

final coalgebra | Fractal Sets as Final Coalgebras Obtained by Completing an Initial Algebra |

finite axiomatization | Derivational modal logic of real line with difference modality |

finite embeddability property | Residuated Lattices, Regular Languages, and Burnside Problem The finite embeddability property for some noncommutative knotted extensions of FL |

finite model property | The finite embeddability property for some noncommutative knotted extensions of FL Almost structural completeness; an algebraic approach An analogue of Bull's theorem for Hybrid Logic A Finite Model Property for Gödel Modal Logics |

finitely presented algebra | Jankov Formula and Ternary Deductive Term |

first-order logic | Scheme representation for first-order logic |

fixpoints | Cuts for circular proofs |

fmp | Derivational modal logic of real line with difference modality |

fractal set | Fractal Sets as Final Coalgebras Obtained by Completing an Initial Algebra |

frame and locale | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

free Boolean extensions and MacNeille completions | Funayama's theorem revisited |

functor semantics | On the constant domains principle and its weakened versions in the Kripke sheaf semantics |

Fuzzy Logic | Two-layer modal logics: from fuzzy logics to a general framework |

Fuzzy Logics | A Finite Model Property for Gödel Modal Logics |

G |

Gabbay-de Jongh logics | A Syntactic Characterization of the Gabbay-de Jongh Logics |

Galois adjunction | A general framework for geometric dualities for varieties of algebras |

GBL-algebras | Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras |

generalized Myhill theorem | Residuated Lattices, Regular Languages, and Burnside Problem |

Glivenko Theorem | A new Glivenko Theorem |

GMV-algebras | Laterally complete and projective hulls of semilinear residuated lattices |

good sequence | Chang-Mundici construction of an enveloping unital lattice-group of a BL-algebra |

Gödel logic | A Finite Model Property for Gödel Modal Logics |

H |

Heyting algebras | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2 |

Higher-Order Modal Logic | General Topos Semantics for Higher-Order Modal Logic |

Hilbert Algebras | Spectral-like duality for Distributive Hilbert Algebras with Infimum |

Hilbert Nullstellensatz | A general framework for geometric dualities for varieties of algebras |

Hilbert space effect-representation | Extensions of ordering sets of states from effect algebras onto their MacNeille completions |

Holland | Cayley and Holland Theorems for Residuated Lattices |

Hopf algebra | Entropic Hopf algebras |

hybrid logic | An analogue of Bull's theorem for Hybrid Logic |

I |

idempotent semimodule | Cayley and Holland Theorems for Residuated Lattices |

idempotent semiring | Cayley and Holland Theorems for Residuated Lattices |

Implicative algebras | Relational groupoids and residuated lattices |

Inductive and Coinductive Types | Cuts for circular proofs |

initial algebra | Fractal Sets as Final Coalgebras Obtained by Completing an Initial Algebra |

initial and final (co)algebras | Cuts for circular proofs |

intermediate logic | A Syntactic Characterization of the Gabbay-de Jongh Logics |

intermediate logics | Jankov Formula and Ternary Deductive Term |

intuitionistic logic | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 1 Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2 |

J |

Jankov characteristic formula | Jankov Formula and Ternary Deductive Term |

join and meet infinite distributive laws | Funayama's theorem revisited |

Jónsson-Tarski algebra | Entropic Hopf algebras |

Jónsson-Tarski duality | Four-valued modal logic: Kripke semantics and duality |

K |

Katetov relation | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

Kripke model | Walker's Cancellation Theorem |

Kripke sheaf semantics | On the constant domains principle and its weakened versions in the Kripke sheaf semantics |

L |

l-group | Chang-Mundici construction of an enveloping unital lattice-group of a BL-algebra |

Lateral Completions | Laterally complete and projective hulls of semilinear residuated lattices |

lattice homomorphism. | On modal components of the S4-logics |

lattice of intermediate logics | On modal components of the S4-logics |

lattice of the normal extensions of the modal logic S4 | On modal components of the S4-logics |

lattice of varieties | Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras |

lattice with antitone involutions | On (finite) distributive lattices with antitone involutions |

Lattice-ordered Abelian group | Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 |

locale | Truncated Vector Lattices |

logical invariance | Tensor products of modal logics |

Lukasiewicz logic | Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 |

M |

MacNeille completion | Extensions of ordering sets of states from effect algebras onto their MacNeille completions |

many-valued modal logic | Four-valued modal logic: Kripke semantics and duality |

Medial algebra | Representation of the Medial-Like Algebras |

metric space | Fractal Sets as Final Coalgebras Obtained by Completing an Initial Algebra |

modal logic | Topological completeness of extensions of S4 Two-layer modal logics: from fuzzy logics to a general framework Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2 |

modal logics | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

modal mu-calculus | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 1 Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2 |

modal product | Tensor products of modal logics |

module | Generalizing the concept of quantum triads |

Moebius transform | MV-Algebraic Moebius Transform on the Vietoris Space |

Monadic algebra | Projectivity and unification in the varieties of locally finite monadic MV-algebras |

monoid | Generalizing the concept of quantum triads |

monotone and antitone functions | A Complete Calculus of Monotone and Antitone Higher-Order Functions |

monotonicity calculus | A Complete Calculus of Monotone and Antitone Higher-Order Functions |

MV-algebra | An elementary proof of the completeness of the Lukasiewicz axioms Projectivity and unification in the varieties of locally finite monadic MV-algebras MV-Algebraic Moebius Transform on the Vietoris Space On (finite) distributive lattices with antitone involutions Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 Chang-Mundici construction of an enveloping unital lattice-group of a BL-algebra Effect algebras with state operator |

MV-effect algebra | Extensions of ordering sets of states from effect algebras onto their MacNeille completions Effect algebras with state operator |

N |

N4-lattices | Priestley duality for (modal) N4-lattices Four-valued modal logic: Kripke semantics and duality |

non-classical logics | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

non-commutative topology | Open projections do not form a right residuated lattice |

Noncommutative residuated lattices | The finite embeddability property for some noncommutative knotted extensions of FL |

normal continuous real function | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

normal frame | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

nuclei and Booleanization | Funayama's theorem revisited |

nucleus | Reducts and Modal Operators on Residuated Lattices |

O |

o-group | Chang-Mundici construction of an enveloping unital lattice-group of a BL-algebra |

observable | Effect algebras, witness pairs and observables |

open projection | Open projections do not form a right residuated lattice |

ordered algebraic structures | Spectral-like duality for Distributive Hilbert Algebras with Infimum |

ordered vector space | Effect algebras with state operator |

orthomodular lattice | Open projections do not form a right residuated lattice |

P |

paraconsistent Nelson logic | Priestley duality for (modal) N4-lattices Four-valued modal logic: Kripke semantics and duality |

Paramedial algebra | Representation of the Medial-Like Algebras |

partially residuated lattice | Open projections do not form a right residuated lattice |

point-set lattice-theoretic topology | On fuzzification of topological categories |

pointfree topology | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

poset model of topological space | Dcpo models of T<sub>1</sub> spaces |

positive linear operators in Hilbert space | Extensions of ordering sets of states from effect algebras onto their MacNeille completions |

powerset theory | On fuzzification of topological categories |

Priestley duality | Priestley duality for (modal) N4-lattices |

projectable completion | Laterally complete and projective hulls of semilinear residuated lattices |

Projectivealgebra | Projectivity and unification in the varieties of locally finite monadic MV-algebras |

Proofs and Types | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

Q |

quantum double | Entropic Hopf algebras |

quasivarieties | Almost structural completeness; an algebraic approach |

R |

reduct | Reducts and Modal Operators on Residuated Lattices |

refutation systems | A Syntactic Characterization of the Gabbay-de Jongh Logics |

regular algebra | Representation of the Medial-Like Algebras |

regular continuous real function | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

Regular element | Representation of the Medial-Like Algebras |

regular language | Residuated Lattices, Regular Languages, and Burnside Problem |

relation algebras | Relevant logic and relation algebras |

Relational Systems | Relational groupoids and residuated lattices |

Relevant logics | Relevant logic and relation algebras |

representation | Cayley and Holland Theorems for Residuated Lattices |

residuated lattice | Residuated Lattices, Regular Languages, and Burnside Problem Cayley and Holland Theorems for Residuated Lattices Reducts and Modal Operators on Residuated Lattices |

residuated lattices | Laterally complete and projective hulls of semilinear residuated lattices Relational groupoids and residuated lattices |

right residuated lattice | Open projections do not form a right residuated lattice |

S |

Sahlqvist correspondence | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 1 |

Sahlvist theory | Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2 |

scattered spaces | On the modal logic of the iterated Cantor derivative and finitary operations on topological spaces |

semicontinuous real function | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

semilattice | Entropic Hopf algebras |

Semilattices | Spectral-like duality for Distributive Hilbert Algebras with Infimum |

sober space | Dcpo models of T<sub>1</sub> spaces |

Specker algebra | Idempotent generated algebras and Boolean powers of commutative rings |

Spectral space | Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 |

state | MV-Algebraic Moebius Transform on the Vietoris Space |

Stone dualities | A general framework for geometric dualities for varieties of algebras |

Stone duality | Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 |

Stone-type dualities | Scheme representation for first-order logic Spectral-like duality for Distributive Hilbert Algebras with Infimum |

strong order unit | Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 |

strongly projectable completion | Laterally complete and projective hulls of semilinear residuated lattices |

sublocale lattice | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |

substructural logics | Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge |

superintuitionistic predicate logics | On the constant domains principle and its weakened versions in the Kripke sheaf semantics |

T |

tensor products of modal logics | Tensor products of modal logics |

topological category | On fuzzification of topological categories |

topological co-axiom | On fuzzification of topological categories |

topological duality | A general framework for geometric dualities for varieties of algebras |

topological semantics | Topological completeness of extensions of S4 |

topological sematics | Derivational modal logic of real line with difference modality |

topological theory | On fuzzification of topological categories |

topos-theoretic semantics | General Topos Semantics for Higher-Order Modal Logic |

tower extension of topological categories | On fuzzification of topological categories |

triad | Generalizing the concept of quantum triads |

twist-structures | Priestley duality for (modal) N4-lattices Four-valued modal logic: Kripke semantics and duality |

two-level syntax | Two-layer modal logics: from fuzzy logics to a general framework |

typed lambda calculus | A Complete Calculus of Monotone and Antitone Higher-Order Functions |

U |

ultraproduct | An elementary proof of the completeness of the Lukasiewicz axioms |

universal algebra | A general framework for geometric dualities for varieties of algebras |

universal topology | On fuzzification of topological categories |

V |

variety with ternary deductive term | Jankov Formula and Ternary Deductive Term |

vector lattice | Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 1 Spectra of finitely presented lattice-ordered Abelian groups and MV-algebras, part 2 |

Visser logic | A new Glivenko Theorem |

W |

Well partially ordered sets | The finite embeddability property for some noncommutative knotted extensions of FL |

witness map | Effect algebras, witness pairs and observables |

Z |

zero continuous real function | Variants of normality and their duals: a pointfree unification of insertion and extension theorems for real-valued functions |