levesque s axiomatization of only knowing is incomplete abstract we show that the axiomatization given by levesque for his logic of only knowing 2 which he showed to be sound and complete for the unquantified version of the logic and conjectured to be complete for the full logic is in fact incomplete

automatic recognition of tractability in inference relations a procedure is given for recognizing sets of inference rules that generate polynomial time decidable inference relations the procedure can automatically recognize the tractability of the inference rules underlying congruence closure the recognition of tractability for that particular rule set constitutes mechanical verification of a theorem originally proved independently by kozen and shostak the procedure is algorithmic rather than heuristic and the class of automatically recognizable tractable rule sets can be precisely characterized a series of examples of rule sets whose tractability is nontrivial yet machine recognizable is also given the technical framework developed here is viewed as a first step toward a general theory of tractable inference relations

locally optimal nonshortening linear covering codes and minimal saturating sets in projective spaces a concept of locally optimal lo linear covering codes is introduced in accordance with the concept of minimal saturating sets in projective spaces over finite fields an lo code is nonshortening in the sense that one cannot remove any column from a parity check matrix without increasing the code covering radius several q sup m concatenating constructions of lo covering codes are described taking a starting lo code as a seed such constructions produce an infinite family of lo codes with the same covering radius the infinite families of lo codes are designed using minimal saturating sets as starting codes new upper bounds on the length function are given new extremal and classification problems for linear covering codes are formulated and investigated in particular the spectrum of possible lengths of lo codes including the greatest possible length the complete computer classification of the minimal saturating sets in small geometries and of the corresponding lo codes is obtained

short codes with a given covering radius the covering radius r of a code is the maximum distance from any vector in the space containing the code to the nearest codeword the authors introduce a new function l m r called the length function which equals the smallest length of a binary code of codimension m and covering radius r they investigate basic properties of the length function projective geometries over larger fields are used to construct families of codes which improve significantly the upper bound for l m 2 obtained by amalgamation of hamming codes general methods are developed for ruling out the existence of codes of covering radius 2 with a given codimension and length resulting in lower bounds for l m 2 a table is presented which gives the best results now known for l m r with m

a semantic characterization of a useful fragment of the situation calculus with knowledge the situation calculus as proposed by mccarthy and hayes and developed over the last decade by reiter and co workers is reconsidered a new logical variant called es is proposed that captures much of the expressive power of the original but where certain technical results are much more easily proved this is illustrated using two existing non trivial results the determinacy of knowledge theorem of reiter and the regression theorem which reduces reasoning about the future to reasoning about the initial situation furthermore we show the correctness of our approach by embedding es in reiter s situation calculus

intruder deduction problem for locally stable theories with normal forms and inverses abstract we present an algorithm to decide the intruder deduction problem idp for a class of equational theories that include associative and commutative ac operators the algorithm is based on the analysis of reductions in the head of terms built from normal contexts using the initial knowledge of the intruder it relies on a new and efficient algorithm to solve a restricted case of higher order ac matching for the subclass of theories for which ac operators have inverses our algorithm runs in polynomial time on the size of a saturated set built from the initial knowledge of the intruder to illustrate we apply the results to pure ac theories abelian groups abelian groups extended with exponentiation and xor although specific algorithms have already been defined to deal with each of these theories we provide a modular approach that can deal with all of them in a uniform way

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

constructions and families of nonbinary linear codes with covering radius 2 new constructions of linear nonbinary codes with covering radius r 2 are proposed they are in part modifications of earlier constructions by the author and in part are new using a starting code with r 2 as a seed these constructions yield an infinite family of codes with the same covering radius new infinite families of codes with r 2 are obtained for all alphabets of size q spl ges 4 and all codimensions r spl ges 3 with the help of the constructions described the parameters obtained are better than those of known codes new estimates for some partition parameters in earlier known constructions are used to design new code families complete caps and other saturated sets of points in projective geometry are applied as starting codes a table of new upper bounds on the length function for q 4 5 7 r 2 and r spl les 24 is included

knowledge action and the frame problem this paper proposes a method for handling the frame problem for knowledge producing actions an example of a knowledge producing action is a sensing operation performed by a robot to determine whether or not there is an object of a particular shape within its grasp the work is an extension of reiter s approach to the frame problem for ordinary actions and moore s work on knowledge and action the properties of our specification are that knowledge producing actions do not affect fluents other than the knowledge fluent and actions that are not knowledge producing only affect the knowledge fluent as appropriate in addition memory emerges as a side effect if something is known in a certain situation it remains known at successor situations unless something relevant has changed also it will be shown that a form of regression examined by reiter for reducing reasoning about future situations to reasoning about the initial situation now also applies to knowledge producing actions

automated complexity analysis based on ordered resolution we define order locality to be a property of clauses relative to a term ordering this property generalizes the subformula property for proofs where the terms appearing in proofs can be bounded under the given ordering by terms appearing in the goal clause we show that when a clause set is order local then the complexity of its ground entailment problem is a function of its structure e g full versus horn clauses and the ordering used we prove that in many cases order locality is equivalent to a clause set being saturated under ordered resolution this provides a means of using standard resolution theorem provers for testing order locality and transforming non local clause sets into local ones we have used the saturate system to automatically establish complexity bounds for a number of nontrival entailment problems relative to complexity classes which include polynomial and exponential time and co np

quasi perfect linear codes with minimum distance 4 some new infinite families of short quasi perfect linear codes are described such codes provide improvements on the currently known upper bounds on the minimal length of a quasi perfect n n m 4 q code when either 1 q 16 m ges 5 m odd or 2 q 2i 7 les i les 15 m ges 4 or 3 q 22lscr lscr ges 8 m ges 5 m odd as quasi perfect n n m 4 q codes and complete n caps in projective spaces pg m 1 q are equivalent objects new upper bounds on the size of the smallest complete cap in pg m 1 q are obtained

semantical considerations on multiagent only knowing abstract levesque introduced the notion of only knowing to precisely capture the beliefs of a knowledge base he also showed how only knowing can be used to formalize nonmonotonic behavior within a monotonic logic levesque s logic only deals with a single agent and therefore a number of attempts have been made to generalize only knowing to the many agent case however all these attempts have some undesirable features most significantly these attempts are propositional and it is not clear how they are to be extended to the first order case in this work we propose a new semantical account of multiagent only knowing which for the first time has a natural possible world semantics for a quantified language with equality among other things properties about levesque s logic generalize faithfully to the many agent case with this account for the propositional fragment we also provide a sound and complete axiomatization finally we obtain a multiagent first order version of the nonmonotonicity exhibited by the logic of only knowing

a model theoretic analysis of knowledge a general semantic model of knowledge is introduced to allow reasoning about statements such as he knows that i know whether or not she knows whether or not it is raining this approach more naturally models a state of knowledge than previous proposals including kripke structures using this notion of model a model theory for knowledge is developed this theory enables one to interpret the notion of a finite amount of information

deciding knowledge in security protocols under equational theories the analysis of security protocols requires precise formulations of the knowledge of protocol participants and attackers in formal approaches this knowledge is often treated in terms of message deducibility and indistinguishability relations in this paper we study the decidability of these two relations the messages in question may employ functions encryption decryption etc axiomatized in an equational theory one of our main positive results says that deducibility and indistinguishability are both decidable in polynomial time for a large class of equational theories this class of equational theories is defined syntactically and includes for example theories for encryption decryption and digital signatures we also establish general decidability theorems for an even larger class of theories these theorems require only loose abstract conditions and apply to many other useful theories for example with blind digital signatures homomorphic encryption xor and other associative commutative functions

binary and ternary linear quasi perfect codes with small dimensions the aim of this work is a systematic investigation of the possible parameters of quasi perfect qp binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes first we give a list of infinite families of qp codes which includes all binary ternary and quaternary codes known to us we continue further with a list of sporadic examples of binary and ternary qp codes later we present the results of our investigation where binary qp codes of dimensions up to 14 and ternary qp codes of dimensions up to 13 are classified

on the decidability and complexity of reasoning about only knowing abstract we study reasoning in levesque s logic of only knowing in particular we first prove that extending a decidable subset of first order logic with the ability of reasoning about only knowing preserves decidability of reasoning as long as quantifying in is not allowed in the language and define a general method for reasoning about only knowing in such a case then we show that the problem of reasoning about only knowing in the propositional case lies at the second level of the polynomial hierarchy thus it is as hard as reasoning in the majority of propositional formalisms for nonmonotonic reasoning like default logic circumscription and autoepistemic logic and it is easier than reasoning in propositional formalisms based on the minimal knowledge paradigm which is strictly related to the notion of only knowing finally we identify a syntactic restriction in which reasoning about only knowing is easier than in the general propositional case and provide a specialized deduction method for such a restricted setting

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

all i know a study in autoepistemic logic abstract current approaches to formalizing nonmonotonic reasoning using logics of belief require the definition of new metalogical properties over sets of sentences this research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic satisfiability validity implication this is done by extending a logic of belief so that it is possible to say that only a certain proposition or finite set of them is believed this research also extends previous approaches to handle quantifiers and equality provides a semantic account of certain types of nonmonotonicity and through a simple proof theory allows formal derivations to be generated

constructions and families of covering codes and saturated sets of points in projective geometry in davydov 1990 constructions of linear binary covering codes were considered in the present paper constructions and techniques of the earlier paper are developed and modified for q ary linear nonbinary covering codes q spl ges 3 and new constructions are proposed the described constructions design an infinite family of codes with covering radius r based on a starting code of the same covering radius for arbitrary r spl ges 2 q spl ges 3 new infinite families of nonbinary covering codes with good parameters are obtained with the help of an iterative process when constructed codes are the starting codes for the following steps the table of upper bounds on the length function for codes with q 3 r 2 3 and codimension up to 24 is given the author proposes to use saturated sets of points in projective geometries over finite fields as parity check matrices of starting codes new saturated sets are obtained

linear codes with covering radius 2 3 and saturating sets in projective geometry infinite families of linear codes with covering radius r 2 3 and codimension tr 1 are constructed on the base of starting codes with codimension 3 and 4 parity check matrices of the starting codes are treated as saturating sets in projective geometry that are obtained by computer search using projective properties of objects upper bounds on the length function and on the smallest sizes of saturating sets are given

generalized possibilistic logic foundations and applications to qualitative reasoning about uncertainty this paper introduces generalized possibilistic logic gpl a logic for epistemic reasoning based on possibility theory formulas in gpl correspond to propositional combinations of assertions such as it is certain to degree that the propositional formula is true as its name suggests the logic generalizes possibilistic logic pl which at the syntactic level only allows conjunctions of the aforementioned type of assertions at the semantic level pl can only encode sets of epistemic states encompassed by a single least informed one whereas gpl can encode any set of epistemic states this feature makes gpl particularly suitable for reasoning about what an agent knows about the beliefs of another agent e g allowing the former to draw conclusions about what the other agent does not know we introduce an axiomatization for gpl and show its soundness and completeness w r t possibilistic semantics subsequently we highlight the usefulness of gpl as a powerful unifying framework for various knowledge representation formalisms among others we show how comparative uncertainty and ignorance can be modelled in gpl we also exhibit a close connection between gpl and various existing formalisms including possibilistic logic with partially ordered formulas a logic of conditional assertions in the style of kraus lehmann and magidor answer set programming and a fragment of the logic of minimal belief and negation as failure finally we analyse the computational complexity of reasoning in gpl identifying decision problems at the first second third and fourth level of the polynomial hierarchy

graph capacities and zero error transmission over compound channels this correspondence investigates the behavior of the compound channel under a zero error constraint we derive expressions for the capacity when a neither the encoder nor decoder has side information about the channel b when only the encoder has such side information these expressions are given in terms of capacities of appropriately defined sets of graphs we clarify that an earlier treatment of the zero error capacity of a compound channel corresponds to the case where the decoder has side information about the channel we also characterize the minimum asymptotic rate for the source coding dual of the compound channel problem namely source coding with compound side information finally we contrast the zero error and asymptotically vanishing error capacities of the compound channel