Costas Koutras - Academia.edu (original) (raw)

Papers by Costas Koutras

Studia Logica - An International Journal for Symbolic Logic, 2001

A new methodology for developing theories of action has recently emerged which provides means for... more A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated.

Journal of Applied Non-classical Logics, 2002

We prove frame determination results for the family of many-valued modal logics introduced by M. ... more We prove frame determination results for the family of many-valued modal logics introduced by M. Fitting in the early '90s. Each modal language of this family is based on a Heyting algebra, which serves as the space of truth values, and is interpreted on an interesting version of possible-worlds semantics: the modal frames are directed graphs whose edges are labelled with an element of the underlying Heyting algebra. We introduce interesting generalized forms of the classical axioms D, T, B, 4, and 5 and prove that they are canonical for certain algebraic frame properties, which generalize seriality, reflexivity, symmetry, transitivity and euclideanness. Our results are quite general as they hold for any modal language built on a complete Heyting algebra.

Logic Journal of The Igpl / Bulletin of The Igpl, 2000

ABSTRACT We contribute to a series of results on the family of many-valued modal logics which has... more ABSTRACT We contribute to a series of results on the family of many-valued modal logics which has been recently introduced by M. Fitting. In this family, the underlying propositional logics employ finite Heyting algebras for the space of truth values and the monotonic modal logics correspond to possible-worlds models with many-valued accessibility relations. There exist also modal nonmonotonic counterparts in the McDermott & Doyle fashion. In Lect. Notes Comput. Sci. 620, 139–150 (1992; Zbl 0978.03518), M. Fitting provided a many-valued generalization of Moore’s autoepistemic logic and proved that, for logics with linear truth spaces, the important theorem of G. Schwarz for the equivalence of K45 and autoepistemic logic extends to the many-valued case. Here, we define and investigate a many-valued generalization of Schwarz’s reflexive autoepistemic logic [G. Schwarz, Fundam. Inform. 17, 157–173 (1992; Zbl 0772.68091)] with an intended interpretation of □ as “true and known”. We prove several interesting properties of many-valued reflexive expansions and show that – under the same linearity restriction – Schwarz’s relevant theorem extends also in the many-valued setting, i.e., our many-valued reflexive autoepistemic logic coincides with many-valued nonmonotonic Sw5.

Journal of Logic and Computation, 2010

ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the famil... more ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We deflne two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy- Milner type theorem. If the underlying algebra H is flnite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our deflnitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

Fundamenta Informaticae, 2009

An important question in modal nonmonotonic logics concerns the limits of propositional definabil... more An important question in modal nonmonotonic logics concerns the limits of propositional definability for logics of the McDermott-Doyle family. Inspired by this technical question we define a variant of autoepistemic logic which provably corresponds to the logic of the McDermott-Doyle family that is based on the modal axiom p5 : 3ϕ ⊃ (¬2ϕ ⊃ 2¬2ϕ). This axiom is a natural weakening of classical negative introspection restricting its scope to possible facts. It closely resembles the axiom w5 : ϕ ⊃ (¬2ϕ ⊃ 2¬2ϕ) which restricts the effect of negative introspection to true facts. We examine p5 in the context of classical possibleworlds Kripke models, providing results for correspondence, completeness and the finite model property. We also identify the corresponding condition for p5 in the context of neighbourhood semantics. Although rather natural epistemically, this axiom has not been investigated in classical modal epistemic reasoning, probably because its addition to S4 gives the well-known strong modal system S5.

Fundamenta Informaticae, 2002

In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language... more In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language is based on an underlying Heyting algebra which provides the space of truth values. The lattice of truth values is explicitly represented in the language by a set of special constants and this allows for forming weak, generalized, many-valued analogs of all classical modal axioms. Weak axioms of this kind have been recently investigated from the canonicity, completeness and correspondence perspective. In this paper, we provide some results on the effect of adopting weak versions of the axioms D, T, 4, 5 and w5 in the family of many-valued modal non-monotonic logics,à la McDermott and Doyle, introduced in [4] and further investigated in . For many-valued modal languages built on finite chains, we extend the results of [7] by proving two quite general range theorems. We then hint on the relation between the modal non-monotonic logics obtained: we prove that there exist ranges which selectively pick out some of the expansions produced by the many-valued autoepistemic logics introduced in , actually the ones with a confidence-bounded set of beliefs. However, an exact characterization of the relation between the various ranges created by the weak many-valued modal axioms still remains to be explored.

Journal of Applied Non-classical Logics, 2005

In this paper we define and examine frame constructions for the family of many-valued modal logic... more In this paper we define and examine frame constructions for the family of many-valued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in . The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. s s s J J J J J J J J J

ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the famil... more ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We deflne two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy- Milner type theorem. If the underlying algebra H is flnite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our deflnitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

ABSTRACT We introduce a suitable notion of bisimulation for the family of Heyting-valued modal lo... more ABSTRACT We introduce a suitable notion of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal lan- guage is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language which is interpreted on relational frames with an H-valued accessibility relation. We prove that for each language, an H-indexed family of bisimulations can be deflned which implies a relative invariance result for the truth values of modal formulas. A bisimula- tion game is further deflned and relevant results, such as the tree model property are examined. If the underlying algebra H is flnite, the modal language can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. In this context, our bisimulations are transformations of H- modal models which guarantee that the epistemic consensus of a predeflned group of the involved experts is invariant under the bisimulation relation.

Studia Logica - An International Journal for Symbolic Logic, 2001

A new methodology for developing theories of action has recently emerged which provides means for... more A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated.

Studia Logica - An International Journal for Symbolic Logic, 2001

A new methodology for developing theories of action has recently emerged which provides means for... more A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated.

Journal of Applied Non-classical Logics, 2002

We prove frame determination results for the family of many-valued modal logics introduced by M. ... more We prove frame determination results for the family of many-valued modal logics introduced by M. Fitting in the early '90s. Each modal language of this family is based on a Heyting algebra, which serves as the space of truth values, and is interpreted on an interesting version of possible-worlds semantics: the modal frames are directed graphs whose edges are labelled with an element of the underlying Heyting algebra. We introduce interesting generalized forms of the classical axioms D, T, B, 4, and 5 and prove that they are canonical for certain algebraic frame properties, which generalize seriality, reflexivity, symmetry, transitivity and euclideanness. Our results are quite general as they hold for any modal language built on a complete Heyting algebra.

Logic Journal of The Igpl / Bulletin of The Igpl, 2000

ABSTRACT We contribute to a series of results on the family of many-valued modal logics which has... more ABSTRACT We contribute to a series of results on the family of many-valued modal logics which has been recently introduced by M. Fitting. In this family, the underlying propositional logics employ finite Heyting algebras for the space of truth values and the monotonic modal logics correspond to possible-worlds models with many-valued accessibility relations. There exist also modal nonmonotonic counterparts in the McDermott & Doyle fashion. In Lect. Notes Comput. Sci. 620, 139–150 (1992; Zbl 0978.03518), M. Fitting provided a many-valued generalization of Moore’s autoepistemic logic and proved that, for logics with linear truth spaces, the important theorem of G. Schwarz for the equivalence of K45 and autoepistemic logic extends to the many-valued case. Here, we define and investigate a many-valued generalization of Schwarz’s reflexive autoepistemic logic [G. Schwarz, Fundam. Inform. 17, 157–173 (1992; Zbl 0772.68091)] with an intended interpretation of □ as “true and known”. We prove several interesting properties of many-valued reflexive expansions and show that – under the same linearity restriction – Schwarz’s relevant theorem extends also in the many-valued setting, i.e., our many-valued reflexive autoepistemic logic coincides with many-valued nonmonotonic Sw5.

Journal of Logic and Computation, 2010

ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the famil... more ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We deflne two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy- Milner type theorem. If the underlying algebra H is flnite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our deflnitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

Fundamenta Informaticae, 2009

An important question in modal nonmonotonic logics concerns the limits of propositional definabil... more An important question in modal nonmonotonic logics concerns the limits of propositional definability for logics of the McDermott-Doyle family. Inspired by this technical question we define a variant of autoepistemic logic which provably corresponds to the logic of the McDermott-Doyle family that is based on the modal axiom p5 : 3ϕ ⊃ (¬2ϕ ⊃ 2¬2ϕ). This axiom is a natural weakening of classical negative introspection restricting its scope to possible facts. It closely resembles the axiom w5 : ϕ ⊃ (¬2ϕ ⊃ 2¬2ϕ) which restricts the effect of negative introspection to true facts. We examine p5 in the context of classical possibleworlds Kripke models, providing results for correspondence, completeness and the finite model property. We also identify the corresponding condition for p5 in the context of neighbourhood semantics. Although rather natural epistemically, this axiom has not been investigated in classical modal epistemic reasoning, probably because its addition to S4 gives the well-known strong modal system S5.

Fundamenta Informaticae, 2002

In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language... more In the family of many-valued modal languages proposed by M. Fitting in 1992, every modal language is based on an underlying Heyting algebra which provides the space of truth values. The lattice of truth values is explicitly represented in the language by a set of special constants and this allows for forming weak, generalized, many-valued analogs of all classical modal axioms. Weak axioms of this kind have been recently investigated from the canonicity, completeness and correspondence perspective. In this paper, we provide some results on the effect of adopting weak versions of the axioms D, T, 4, 5 and w5 in the family of many-valued modal non-monotonic logics,à la McDermott and Doyle, introduced in [4] and further investigated in . For many-valued modal languages built on finite chains, we extend the results of [7] by proving two quite general range theorems. We then hint on the relation between the modal non-monotonic logics obtained: we prove that there exist ranges which selectively pick out some of the expansions produced by the many-valued autoepistemic logics introduced in , actually the ones with a confidence-bounded set of beliefs. However, an exact characterization of the relation between the various ranges created by the weak many-valued modal axioms still remains to be explored.

Journal of Applied Non-classical Logics, 2005

In this paper we define and examine frame constructions for the family of many-valued modal logic... more In this paper we define and examine frame constructions for the family of many-valued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in . The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. s s s J J J J J J J J J

ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the famil... more ABSTRACT We examine the notion of bisimulation and its ramiflcations, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We deflne two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy- Milner type theorem. If the underlying algebra H is flnite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our deflnitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

ABSTRACT We introduce a suitable notion of bisimulation for the family of Heyting-valued modal lo... more ABSTRACT We introduce a suitable notion of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal lan- guage is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language which is interpreted on relational frames with an H-valued accessibility relation. We prove that for each language, an H-indexed family of bisimulations can be deflned which implies a relative invariance result for the truth values of modal formulas. A bisimula- tion game is further deflned and relevant results, such as the tree model property are examined. If the underlying algebra H is flnite, the modal language can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. In this context, our bisimulations are transformations of H- modal models which guarantee that the epistemic consensus of a predeflned group of the involved experts is invariant under the bisimulation relation.

Studia Logica - An International Journal for Symbolic Logic, 2001

A new methodology for developing theories of action has recently emerged which provides means for... more A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated.