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Papers by Janusz Czelakowski

Research paper thumbnail of Reguły działania a argumentacja

Reguły działania a argumentacja 1 Abstrakt. Argumentacja niemonotoniczna ma być blisko rozumowań ... more Reguły działania a argumentacja 1 Abstrakt. Argumentacja niemonotoniczna ma być blisko rozumowań praktycznych i zdroworozsądkowych: wykonawcy czynności (agenci) opracowują plany działań i starają się plany te wykonać; często jednak są pozbawieni pełnego opisu sytuacji, ich wiedza jest cząstkowa, czynią założenia i podejmują decyzje oraz działania, w tym działania słowne, polegając na własnym doświadczeniu i nawykach. Powstające formalne struktury obejmują tzw. cyrkumskrypcje (circumscriptions), logikę domyśleń (default logic), logikę autoepistemiczną (autoepistemic logic), konsekwencje kumulatywne (cumulative consequences) i szereg innych. Można wyodrębnić dwa główne typy systemów rozumowań niemonotonicznych: systemy defi niowalne poprzez modele kumulatywne lub preferencyjne oraz logiki domyśleń. W artykule szkicujemy inne ujęcie zagadnienia, w którym centralną rolę gra pojęcie reguły działania (rule of conduct); inaczej: reguły pragmatycznej. Zgodnie z nim, argumentacja niemonotoniczna jest wsparta na konsekwencjach przyjętych reguł działania. Stan rzeczy jest wyprowadzony ze skończonego zbioru przesłanek, gdy czynności obejmowane daną regułą działania prowadzą do stanu rzeczy będącego wnioskiem reguły. (Przesłankę identyfi kuje się tu ze zbiorem stanów rzeczy.) W odróżnieniu od reguł logiki (tj. reguł inferencji) reguły działania nie są dane raz na zawsze; mogą być modyfi kowane, niekiedy są zawodne, a nawet mogą być odrzucane i zastępowane nowymi. Artykuł zawiera rozszerzone i rozbudowane oryginalne wątki naszkicowane w monografi i Czelakowskiego (2015). Celem artykułu jest przybliżenie ich polskiemu czytelnikowi. Słowa kluczowe: działanie, układ działania, drzewo etykietowane, reguła działania, rama, operacja wynikania Rules of action and argumentation Abstract. The approach to non-monotonic reasonings based on rules of conduct is presented. Each rule of conduct is a systems of actions the agents are obeyed to in the circumstances pertaining to the rule. Rules of conducts are not given for ever; they may be modifi ed or even rejected and replaced by new ones. According to this approach, non-monotonic arguments are those which do not violate the actions involve in these rules. A conclusion is reached from a fi nite set of premises, each premiss identifi es with a set of states, if the actions involved in a rule of conduct yield a set of affairs being the conclusion of the rule. The article contains original extended versions of remarks outlined in Czelakowski (2015).

Research paper thumbnail of Rasiowa–Sikorski Sets and Forcing

The paper is concerned with the problem of building models for first-order languages from the per... more The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski (1950). The central idea, due to Rasiowa and Sikorski and developed in this paper, is constructing first-order models from individual variables. The notion of a Rasiowa–Sikorski set of formulas of an arbitrary language L is introduced. Investigations are confined to countable languages. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, each countable model for L is determined, up to isomorphism, by some Rasiowa–Sikorski set. Consequences of these facts are investigated.

Research paper thumbnail of AC is Equivalent to the Coherence Principle. Corrigendum to my Paper "Induction Principles for Sets

Fundamenta Informaticae, 2009

ABSTRACT Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property f... more ABSTRACT Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property for partial functions contained in a relation are formulated. The equivalence of the coherent principles with AC and the equivalence of the ultrafilter property with BPI is shown.

Research paper thumbnail of Abstrakcyjna logika algebraiczna pomostem między algebrą a logiką

Wiadomości Matematyczne, 2017

Research paper thumbnail of Partial Boolean algebras in a broader sense and Boolean embeddings

Colloquium Mathematicum, 1981

Research paper thumbnail of On extending of partial Boolean algebras to partial *-algebras

Colloquium Mathematicum, 1978

Research paper thumbnail of Remarks on finitely based logics

Lecture Notes in Mathematics, 1984

ABSTRACT Without Abstract

Research paper thumbnail of Epistemic Aspects of Action Systems

Trends in Logic, 2015

The theory of action conventionally distinguishes real actions and doxastic (or epistemic) action... more The theory of action conventionally distinguishes real actions and doxastic (or epistemic) actions. Real actions (or as we put it—praxeological actions) bring about changes in material objects of the environment external to the agent. Epistemic actions concern mental states of agents—they bring about changes of agents’ knowledge or beliefs about the environment as well as about other beliefs. Some logical issues concerning knowledge, action, truth, and the epistemic status of agents are discussed. In this context the frame and ramification problems are also analyzed. The key issue raised in this chapter is that of non-monotonicity of reasoning. A reasoning is non-monotonic if some conclusions are invalidated by adding more knowledge. In this chapter a semantic approach to non-monotonic forms of reasoning, combining them with action theory, is presented. It is based on the notions of a frame and of a (tree-like) rule of conduct for an action system.

Research paper thumbnail of Reduced products of logical matrices

Studia Logica, 1980

The class Mat~'(C) of all matrices for a propositional logic (Lz, C) is investigated. The paper c... more The class Mat~'(C) of all matrices for a propositional logic (Lz, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matt(C) states the following. Assume C to be the consequence operation on a propositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of G. Then Matt (C) is the least class of matrices containing K and Closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images.

Research paper thumbnail of Situational Action Systems

Trends in Logic, 2015

Situational aspects of action are discussed. The presented approach emphasizes the role of situat... more Situational aspects of action are discussed. The presented approach emphasizes the role of situational contexts in which actions are performed. These contexts influence the course of an action; they are determined not only by the current state of the system but also shaped by other factors as time, the previously undertaken actions and their succession, the agents of actions and so on. The distinction between states and situations is explored from the perspective of action systems. The notion of a situational action system is introduced and its theory is expounded. Numerous examples illustrate the reach of the theory.

Research paper thumbnail of Monotone Relations, Fixed Points and Recursive Definitions

Towards Mathematical Philosophy

The paper is concerned with reflexive points of relations. The significance of reflexive points i... more The paper is concerned with reflexive points of relations. The significance of reflexive points in the context of indeterminate recursion principles is shown.

Research paper thumbnail of Elements of Formal Action Theory

Research paper thumbnail of A note on the extension principle for relatively congruence-distributive quasivarieties

Bulletin of the Section of Logic

Research paper thumbnail of The Equationally-Defined Commutator

This monograph introduces and explores the notions of a commutator equation and the equationally-... more This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras. The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic

Research paper thumbnail of John F. Horthy, Agency and Deontic Logic

Research paper thumbnail of Induction Principles for Sets

Fundamenta Informaticae

We show that a family of tree languages W_{(l,k)}, previously used by J. Bradfield, and by the fi... more We show that a family of tree languages W_{(l,k)}, previously used by J. Bradfield, and by the first author to show the strictness of the Rabin¨CMostowski index hierarchy of alternating tree automata, forms a hierarchy w.r.t. theWadge reducibility. ...

Research paper thumbnail of Algebraizable Logics

Research paper thumbnail of Regularly Algebraizable Logics

Trends in Logic, 2001

A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a no... more A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a non-empty system E(p, q) of equivalence sentences such that E(p, q) ⊆ C(p, q).

Research paper thumbnail of 24th European Summer School on Logic, Language and Information (ESSLLI 2012), Opole University, Opole, Poland, August 6—17, 2012

Bulletin of Symbolic Logic, 2013

Research paper thumbnail of Local deductions theorems

Studia Logica, 1986

The notion of local deduction theorem (which generalizes on the known instances of indeterminate ... more The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued Lukasiewicz logic C8) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).

Research paper thumbnail of Reguły działania a argumentacja

Reguły działania a argumentacja 1 Abstrakt. Argumentacja niemonotoniczna ma być blisko rozumowań ... more Reguły działania a argumentacja 1 Abstrakt. Argumentacja niemonotoniczna ma być blisko rozumowań praktycznych i zdroworozsądkowych: wykonawcy czynności (agenci) opracowują plany działań i starają się plany te wykonać; często jednak są pozbawieni pełnego opisu sytuacji, ich wiedza jest cząstkowa, czynią założenia i podejmują decyzje oraz działania, w tym działania słowne, polegając na własnym doświadczeniu i nawykach. Powstające formalne struktury obejmują tzw. cyrkumskrypcje (circumscriptions), logikę domyśleń (default logic), logikę autoepistemiczną (autoepistemic logic), konsekwencje kumulatywne (cumulative consequences) i szereg innych. Można wyodrębnić dwa główne typy systemów rozumowań niemonotonicznych: systemy defi niowalne poprzez modele kumulatywne lub preferencyjne oraz logiki domyśleń. W artykule szkicujemy inne ujęcie zagadnienia, w którym centralną rolę gra pojęcie reguły działania (rule of conduct); inaczej: reguły pragmatycznej. Zgodnie z nim, argumentacja niemonotoniczna jest wsparta na konsekwencjach przyjętych reguł działania. Stan rzeczy jest wyprowadzony ze skończonego zbioru przesłanek, gdy czynności obejmowane daną regułą działania prowadzą do stanu rzeczy będącego wnioskiem reguły. (Przesłankę identyfi kuje się tu ze zbiorem stanów rzeczy.) W odróżnieniu od reguł logiki (tj. reguł inferencji) reguły działania nie są dane raz na zawsze; mogą być modyfi kowane, niekiedy są zawodne, a nawet mogą być odrzucane i zastępowane nowymi. Artykuł zawiera rozszerzone i rozbudowane oryginalne wątki naszkicowane w monografi i Czelakowskiego (2015). Celem artykułu jest przybliżenie ich polskiemu czytelnikowi. Słowa kluczowe: działanie, układ działania, drzewo etykietowane, reguła działania, rama, operacja wynikania Rules of action and argumentation Abstract. The approach to non-monotonic reasonings based on rules of conduct is presented. Each rule of conduct is a systems of actions the agents are obeyed to in the circumstances pertaining to the rule. Rules of conducts are not given for ever; they may be modifi ed or even rejected and replaced by new ones. According to this approach, non-monotonic arguments are those which do not violate the actions involve in these rules. A conclusion is reached from a fi nite set of premises, each premiss identifi es with a set of states, if the actions involved in a rule of conduct yield a set of affairs being the conclusion of the rule. The article contains original extended versions of remarks outlined in Czelakowski (2015).

Research paper thumbnail of Rasiowa–Sikorski Sets and Forcing

The paper is concerned with the problem of building models for first-order languages from the per... more The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski (1950). The central idea, due to Rasiowa and Sikorski and developed in this paper, is constructing first-order models from individual variables. The notion of a Rasiowa–Sikorski set of formulas of an arbitrary language L is introduced. Investigations are confined to countable languages. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, each countable model for L is determined, up to isomorphism, by some Rasiowa–Sikorski set. Consequences of these facts are investigated.

Research paper thumbnail of AC is Equivalent to the Coherence Principle. Corrigendum to my Paper "Induction Principles for Sets

Fundamenta Informaticae, 2009

ABSTRACT Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property f... more ABSTRACT Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property for partial functions contained in a relation are formulated. The equivalence of the coherent principles with AC and the equivalence of the ultrafilter property with BPI is shown.

Research paper thumbnail of Abstrakcyjna logika algebraiczna pomostem między algebrą a logiką

Wiadomości Matematyczne, 2017

Research paper thumbnail of Partial Boolean algebras in a broader sense and Boolean embeddings

Colloquium Mathematicum, 1981

Research paper thumbnail of On extending of partial Boolean algebras to partial *-algebras

Colloquium Mathematicum, 1978

Research paper thumbnail of Remarks on finitely based logics

Lecture Notes in Mathematics, 1984

ABSTRACT Without Abstract

Research paper thumbnail of Epistemic Aspects of Action Systems

Trends in Logic, 2015

The theory of action conventionally distinguishes real actions and doxastic (or epistemic) action... more The theory of action conventionally distinguishes real actions and doxastic (or epistemic) actions. Real actions (or as we put it—praxeological actions) bring about changes in material objects of the environment external to the agent. Epistemic actions concern mental states of agents—they bring about changes of agents’ knowledge or beliefs about the environment as well as about other beliefs. Some logical issues concerning knowledge, action, truth, and the epistemic status of agents are discussed. In this context the frame and ramification problems are also analyzed. The key issue raised in this chapter is that of non-monotonicity of reasoning. A reasoning is non-monotonic if some conclusions are invalidated by adding more knowledge. In this chapter a semantic approach to non-monotonic forms of reasoning, combining them with action theory, is presented. It is based on the notions of a frame and of a (tree-like) rule of conduct for an action system.

Research paper thumbnail of Reduced products of logical matrices

Studia Logica, 1980

The class Mat~'(C) of all matrices for a propositional logic (Lz, C) is investigated. The paper c... more The class Mat~'(C) of all matrices for a propositional logic (Lz, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matt(C) states the following. Assume C to be the consequence operation on a propositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of G. Then Matt (C) is the least class of matrices containing K and Closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images.

Research paper thumbnail of Situational Action Systems

Trends in Logic, 2015

Situational aspects of action are discussed. The presented approach emphasizes the role of situat... more Situational aspects of action are discussed. The presented approach emphasizes the role of situational contexts in which actions are performed. These contexts influence the course of an action; they are determined not only by the current state of the system but also shaped by other factors as time, the previously undertaken actions and their succession, the agents of actions and so on. The distinction between states and situations is explored from the perspective of action systems. The notion of a situational action system is introduced and its theory is expounded. Numerous examples illustrate the reach of the theory.

Research paper thumbnail of Monotone Relations, Fixed Points and Recursive Definitions

Towards Mathematical Philosophy

The paper is concerned with reflexive points of relations. The significance of reflexive points i... more The paper is concerned with reflexive points of relations. The significance of reflexive points in the context of indeterminate recursion principles is shown.

Research paper thumbnail of Elements of Formal Action Theory

Research paper thumbnail of A note on the extension principle for relatively congruence-distributive quasivarieties

Bulletin of the Section of Logic

Research paper thumbnail of The Equationally-Defined Commutator

This monograph introduces and explores the notions of a commutator equation and the equationally-... more This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras. The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic

Research paper thumbnail of John F. Horthy, Agency and Deontic Logic

Research paper thumbnail of Induction Principles for Sets

Fundamenta Informaticae

We show that a family of tree languages W_{(l,k)}, previously used by J. Bradfield, and by the fi... more We show that a family of tree languages W_{(l,k)}, previously used by J. Bradfield, and by the first author to show the strictness of the Rabin¨CMostowski index hierarchy of alternating tree automata, forms a hierarchy w.r.t. theWadge reducibility. ...

Research paper thumbnail of Algebraizable Logics

Research paper thumbnail of Regularly Algebraizable Logics

Trends in Logic, 2001

A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a no... more A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a non-empty system E(p, q) of equivalence sentences such that E(p, q) ⊆ C(p, q).

Research paper thumbnail of 24th European Summer School on Logic, Language and Information (ESSLLI 2012), Opole University, Opole, Poland, August 6—17, 2012

Bulletin of Symbolic Logic, 2013

Research paper thumbnail of Local deductions theorems

Studia Logica, 1986

The notion of local deduction theorem (which generalizes on the known instances of indeterminate ... more The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued Lukasiewicz logic C8) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).