George Voutsadakis Assistant Professor (with Tenure) School of Mathematics and Computer Science Lake Superior State University

Research Interests

• Algebraic Logic
• Categorical and Universal Algebra
• Ordered Structures
  
• Modular Description Logics
• Privacy-Preserving Reasoning
  

Mathematical Genealogy

Monograph in Progress

• Categorical Abstract Algebraic Logic: Hierarchies of π-Institutions
  
  

Technical Reports

• On Some Operations on Classes of Algebras and Coalgebras from a Bialgebraic Viewpoint pdf or postscript
• Probablistic Threshold Agent Networks pdf or postscript
• On the Categorical Mobius Calculus pdf   or postscript
• Combinatorial Analysis of the State Space Structure of Finite Automata Networks pdf or postscript
• Privacy-Preserving Reasoning for Hypergraphical Knowledge Bases (with Jie Bao, Giora Slutzki and Vasant Honavar) pdf or postscript
• Secrecy Preserving Reasoning Over Entailment Systems Theory and Applications (with Giora Slutzki and Vasant Honavar) pdf or postscript
• Secrecy Preserving Reasoning Using Secrecy Envelopes (with Giora Slutzki and Vasant Honavar) pdf or postscript

Preprints

• Algebraic Logic
• Categorical Abstract Algebraic Logic: Operations on Classes of Models pdf or postscript
• Categorical Abstract Algebraic Logic: Weakly Algebraizable π-Institutions pdf or postscript
• Categorical Abstract Algebraic Logic: Selfextensional π-Institutions with Implication pdf or postscript
• Categorical Abstract Algebraic Logic: Selfextensional π-Institutions with Conjunction pdf or postscript
• Categorical Abstract Algebraic Logic: Local Deduction Theorems for π-Institutions pdf or postscript
• Categorical Abstract Algebraic Logic: Fibring of π-Institutions pdf or postscript
• Categorical Abstract Algebraic Logic: Equivalence of Closure Systems pdf or postscript
• Categorical Abstract Algebraic Logic: Protoalgebraic Classes of Structure Systems pdf or postscript
• Categorical Abstract Algebraic Logic: Compatibility Operators and the Leibniz Hierarchy pdf or postscript
• Categorical Abstract Algebraic Logic: The Subdirect Product Theorem pdf or postscript
• Categorical Abstract Algebraic Logic: Pragmatic Matrix System Semantics pdf or postscript
• Categorical Abstract Algebraic Logic: Multi-Valued Referential Matrix System Semantics pdf or postscript

• Algebra
• Equational and Metaequational Theories and Semantic and Syntactic Varieties of Algebraic Systems pdf or postscript
• Quasi- and Guasi-Equational Theories and Quasi- and Guasi-Varieties of Algebraic Systems pdf or postscript
  
  


• Order
• An  Equational Theory of n-Lattices pdf or postscript
• Chu Spaces, Concept Lattices and Information Systems in n Dimensions pdf or postscript

 
• Modular Description Logics
• Distributed Reasoning with Modular Ontologies (with Jie Bao, Giora Slutzki and Vasant Honavar) pdf or postscript
• Package-based Description Logics: Syntax, Semantics and Complexity (with Jie Bao, Giora Slutzki and Vasant Honavar) pdf or postscript
  
• F-ALCI: A Fully Contextualized, Federated Logic for the Semantic Web (with Jie Bao, Giora Slutzki and Vasant Honavar) pdf or postscript
• A Federated Tableau Algorithm for F-ALCI (with Giora Slutzki, Jie Bao and Vasant Honavar) pdf or postscript
• Reasoning with F-ALCI Over Lattices (with Giora Slutzki and Vasant Honavar) pdf or postscript
  

Papers 

• A Duality Theory for Bilattices, Algebra Universalis, 43 (2000), 109-125. (with B. Mobasher, D. Pigozzi, and G. Slutzki). pdf
• Categorical Abstract Algebraic Logic: Algebraizable Institutions, Applied Categorical Structures, 10 (6) (2002), 531-568. pdf  
• Polyadic Concept Analysis, Order, 19 (3) (2002), 295-304 pdf
• Categorical Models and Quasigroup Homotopies , Theory and Applications of Categories, 11 (1) (2003), 1-14 pdf , ps , dvi
• Threshold Agent Networks An Approach to Modelling and Simulation, Applied Mathematics and Computation, 142 (2003), 521-543 pdf 
  
• Categorical Abstract Algebraic Logic: Metalogical Properties , Studia Logica, 74 (2003), 369-398 pdf , ps
• Categorical Abstract Algebraic Logic: Equivalent Institutions, Studia Logica, 74 (2003), 275-311 pdf
• A Categorical Construction of a Variety of Clone Algebras, Scientiae Mathematicae Japonicae, 59 (2) (2004), 339-349, :e9, 79-89 pdf
• A Categorical Approach to Threshold Agent Networks,  Applied Categorical Structures, 12 (2) (2004), 203-223 pdf
• On the Categorical Algebras of First-Order Logic, Scientiae Mathematicae Japonicae, 60 (1) (2004), 37-44, :e10, 47-54 pdf
• On the Limit Cycle Structure of Threshold Boolean Networks over Complete Graphs, International Journal of Neural Systems, 14 (3) (2004), 209-215 pdf
• The Categories of Finitary Binary Functions and Finite Automata Networks, Scientiae Mathematicae Japonicae, 11 (2004), 233-240 pdf
• Categorical Abstract Algebraic Logic: Categorical Algebraization of Equational Logic, Logic Journal of the IGPL, 12 (4) (2004), 313-333 pdf or postscript  
• Categorical Abstract Algebraic Logic: Categorical Algebraization of First-order Logic Without Terms, Archive for Mathematical Logic, 44 (4) (2005), 473-491 pdf
• Categorical Abstract Algebraic Logic: Protoalgebraicity and Leibniz Theory Systems, Scientiae Mathematicae Japonicae, 62 (1) (2005), 109-117 pdf
  
• Remarks on Classifications and Adjunctions, Rendiconti del Circolo Matematico di Palermo, 54 (2) (2005), 50-70 pdf 
• Categorical Abstract Algebraic Logic: (I, N)-Algebraic Systems, Applied Categorical Structures, 13 (3) (2005), 265-280 pdf
  
• Categorical Abstract Algebraic Logic: Gentzen π-Institutions and the Deduction-Detachment Property, Mathematical Logic Quarterly, 51 (6) (2005), 570-578 pdf
• Categorical Abstract Algebraic Logic: Models of  π-Institutions, Notre Dame Journal of Formal Logic, 46 (4) (2005), 439-460 pdf
• Categorical Abstract Algebraic Logic: Partially Ordered Algebraic Systems, Applied Categorical Structures, 14 (1) (2006), 81-98 pdf
• Categorical Abstract Algebraic Logic: The Largest Theory System Included in a Theory Family, Mathematical Logic Quarterly, 52 (3) (2006), 288-294 pdf
• Categorical Abstract Algebraic Logic: Full Models, Frege Systems and Metalogical Properties, Reports on Mathematical Logic, 41 (2006), 31-62 pdf
  
• n-Closure Systems and n-Closure Operators, Algebra Universalis, 55 (2006), 369-386 pdf
• Categorical Abstract Algebraic Logic: Leibniz Equality and Homomorphism Theorems, Applied Categorical Structures, 14 (4) (2006), 357-376 pdf
• Categorical Abstract Algebraic Logic: More on Protoalgebraicity, Notre Dame Journal of Formal Logic, 47 (4) (2006), 487-514 pdf
  
• Categorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties, Order, 23 (4) (2006), 297-319  pdf
• Categorical Abstract Algebraic Logic: Structure Systems and Łoś' Theorem, Far East Journal of Mathematical Sciences, 24 (1) (2007), 73-98 pdf or postscript
• Categorical Abstract Algebraic Logic: Subdirect Representation of Pofunctors, Communications in Algebra, 35 (1) (2007), 1-10 pdf
  
• Categorical Abstract Algebraic Logic: Operators On Classes of Structure Systems, Scientiae Mathematicae Japonicae, 65 (1) (2007), 11-25, :e2006, 1009-1023 pdf
• Categorical Abstract Algebraic Logic: The Diagram and Reduction Operator Lemmas, Mathematical Logic Quarterly, 53 (2) (2007), 147-161 pdf 
• Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity, Studia Logica, 85 (2) (2007), 215-249 pdf
• Categorical Abstract Algebraic Logic: Strong Version of a Protoalgebraic π-Institution, Reports on Mathematical Logic, 42 (2007), 19-46 pdf
• Categorical Abstract Algebraic Logic: Gentzen π-institutions, Scientiae Mathematicae Japonicae, 66 (2) (2007), 227-242, :e2007, 407-422 pdf
  
• Categorical Abstract Algebraic Logic: The Categorical Suszko Operator, Mathematical Logic Quarterly, 53 (6) (2007), 616-635 pdf 
• Dedekind-MacNeille Completion of n-Ordered Sets, Order, 24 (1) (2007), 15-29 pdf
• Categorical Abstract Algebraic Logic: Equivalential π-Institutions, Australasian Journal of Logic, 6 (2008), 24pp pdf
• Categorical Abstract Algebraic Logic: Bloom's Theorem for Rule-Based π-Institutions, Logic Journal of the IGPL, 16 (3) (2008), 233-248 pdf or postscript
• Categorical Abstract Algebraic Logic: Local Characterization Theorems for Classes of Systems, Communications in Algebra, 36 (8) (2008), 3093-3112 pdf
• Categorical Abstract Algebraic Logic: Structurality, Protoalgebraicity and Correspondence, Mathematical Logic Quarterly, 55 (1) (2009), 51-67 pdf
• Categorical Abstract Algebraic Logic: Syntactically Algebraizable π-Institutions, Reports on Mathematical Logic, 44 (2009), 105-151 pdf
• Categorical Abstract Algebraic Logic: Subdirect Representation for Classes of Structure Systems, Advances and Applications in Mathematical Sciences, 1 (1) (2009), 37-64 pdf
• Package-based Description Logics, in Modular Ontologies, H. Stuckenschmidt et al. (eds.), Lecture Notes in Computer Science, 5445 (2009), 349-371 (with Jie Bao, Giora Slutzki and Vasant Honavar) pdf
• Universal Dialgebra: Unifying Universal Algebra and Coalgebra, Far East Journal of Mathematical Sciences, 44 (1) (2010), 1-53 pdf or postscript
• Probabilistic Federated ALCI, Advances in Computer Science and Engineering, 5 (2) (2010), 131-172 pdf
• Categorical Abstract Algebraic Logic: On Admissible Equivalence Systems, Advances and Applications in Mathematical Sciences, 10 (6) (2011), 583-604 pdf
• Secrecy Logic: S-Secrecy Structures, Turkish Journal of Mathematics, 36 (1) (2012), 1-27 pdf (extended preprint version pdf)
• Categorical Abstract Algebraic Logic: Closure Operators on Classes of PoFunctors, Armenian Journal of Mathematics, 4 (1) (2012), 1-24 pdf
• Secrecy Logic: Protoalgebraic S-Secrecy Logics, Reports on Mathematical Logic, 47 (2012), 3-28 pdf
• F-ALCIK: Fully Contextualized Federated ALCI with Epistemic Operators, Advances in Computer Science and Engineering, 8 (1) (2012), 1-30 pdf or postscript
• Categorical Abstract Algebraic Logic: Coordinatization is Algebraization, Reports on Mathematical Logic, 47 (2012), 125-145 pdf
• Categorical Abstract Algebraic Logic: Generalized Tarski Congruence Systems, Advances in Mathematics Research, 17 (2012) pdf or postscript
• Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems, Journal of Mathematics, 2013 (2013), 8pp pdf
• Categorical Abstract Algebraic Logic: Algebraic Semantics for π-Institutions, Mathematical Logic Quarterly, 59 (3) (2013), 177-200 pdf
• Categorical Abstract Algebraic Logic: Referential Algebraic Semantics, Studia Logica, 101 (4) (2013), 849-899 pdf
• Malinowski Modalization, Modalization through Fibring and the Leibniz Hierarchy (with Manuel António Martins), Logic Journal of the IGPL, 21 (5) (2013), 836-852 pdf
• Categorical Abstract Algebraic Logic: Behavioral π-Institutions, Studia Logica, 102 (3) (2014), 617-646 pdf
• Categorical Abstract Algebraic Logic: Cryptofibring of Logical Systems, Advances and Applications in Mathematical Sciences, 13 (4) (2014), 155-194 pdf
• Categorical Abstract Algebraic Logic: Truth Equational π-Institutions, Notre Dame Journal of Formal Logic, 56 (2) (2015), 351-378 pdf
• Categorical Abstract Algebraic Logic: Referential π-Institutions, Bulletin of the Section of Logic, 44 (1/2) (2015), 33-51 pdf
• Categorical Abstract Algebraic Logic: Tarski Congruence Systems, Logical Morphisms and Logical Quotients, Journal of Pure and Applied Mathematics: Advances and Applications, 13 (1) (2015), 27-73 pdf
• Categorical Abstract Algebraic Logic: Skywatching in Semilattice Systems, Logic Journal of the IGPL, 24 (2) (2016), 138-155 pdf
• Categorical Abstract Algebraic Logic: Weakly Referential π-Institutions, Reports on Mathematical Logic, 51 (2016), 91-103 pdf
• Categorical Abstract Algebraic Logic: Hidden Multi-Sorted Logics as Multi-Term π-Institutions, Bulletin of the Section of Logic, 45 (2) (2016), 111-124 pdf
• Categorical Abstract Algebraic Logic: Wójcicki's Conjecture and Malinowski's Theorem, Reports on Mathematical Logic, 52 (2017), 69-82 pdf
  
• Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems, ``Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science", J. Czelakowski (ed.), Outstanding Contributions to Logic, Volume 16, Springer 2018, 421-454 pdf
• Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics, Bulletin of the Section of Logic, 47 (2) (2018), 69-88 pdf
  

Non-Papers

• Categorical Abstract Algebraic Logic: the criterion for deductive equivalence, Mathematical Logic Quarterly, 49 (4) (2003), 347-352 pdf
  
• Corrigendum to "Categorical abstract algebraic logic: The criterion for deductive equivalence", Mathematical Logic Quarterly, 51 (6) (2005), 644-644 pdf

• Categorical Abstract Algebraic Logic, Ph.D. Dissertation, Iowa State University, Ames, IA, 1998 pdf
  
• Federated Description Logics for the Semantic Web, Ph.D. Dissertation, Iowa State University, Ames, IA, 2010 pdf

• On The Decidability of Role Mappings Between Modular Ontologies (with Jie Bao, Giora Slutzki and Vasant Honavar), Twenty-Third AAAI Conference on Artificial Intelligence (AAAI-08), July 13-17, Chicago, Illinois, USA pdf or postscript
• Federated ALCI: Preliminary Report (with Jie Bao, Giora Slutzki and Vasant Honavar), International Conference on Intelligent Agent Technology (WI'08), December 9-12, Sydney, Australia (Short Paper) pdf or postscript
• Package-based Description Logics, in Modular Ontologies, H. Stuckenschmidt et al. (eds.), Lecture Notes in Computer Science, 5445 (2009), 349-371 (with Jie Bao, Giora Slutzki and Vasant Honavar) pdf
• Comparing Availability in Controlled Query Evaluation Using Unordered Query Evaluation for Known Potential Secrets, International Workshop on Logic in Databases (LID 2009), October 29, Roskilde University, Denmark pdf or postscript