minimal knowledge problem a new approach abstract in this paper we propose a new logic of minimal knowledge our approach falls into the general scheme of shoham s preference semantics it stems from an earlier work on logics of minimal knowledge by halpern and moses lin and shoham and lifschitz the novelty of our work is in a procedure for minimizing knowledge which we propose in this paper and which is different from earlier proposals we show that our logic preserves most desirable properties of earlier formalisms and at the same time avoids some of their drawbacks in addition to a semantic definition of our system we provide its equivalent syntactic characterization which relates our logic with the nonmonotonic modal logic s4f and allows us to use in our investigations standard modal logic techniques

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

minimal belief and negation as failure abstract fangzhen lin and yoav shoham defined a propositional nonmonotonic logic which uses two independent modal operators one of them represents minimal knowledge the other is related to the ideas of justification as understood in default logic and of negation as failure we describe a simplified version of that system show how quantifiers can be included in it and study its relation to circumscription and default logic to logic programming and to the theory of epistemic queries developed by hector levesque and ray reiter

limited reasoning in first order knowledge bases abstract in traditional formal approaches to knowledge representation agents are assumed to believe all the logical consequences of their knowledge bases as a result reasoning in the first order case becomes undecidable since real agents are constrained by resource limitations it seems appropriate to look for weaker forms of reasoning with better computational properties one way to approach the problem is by modeling belief reasoning can then be understood as the question whether a belief follows from believing the sentences in the knowledge base this paper proposes a model of belief which combines features from both possible world semantics and relevance logic among the important features of this logic are its treatment of quantifying in which allows us to distinguish between knowing that and knowing who and the decidability of the implication problem for belief the decidability result follows from a close connection between this notion of belief and an existing decidable form of first order entailment

overflow underflow free floating point number representations with self delimiting variable length exponent field a class of new floating point representations of real numbers based on representations of the integers is described in the class every representation uses a self delimiting representation of the integers as a variable length field of the exponent and neither overflow nor underflow appears in practice the adopted representations of the integers are defined systematically so that representation s of numbers greater than one have both exponent significant and integer fraction interpretations since representation errors are characterized by the length function of an underlying representation of the integers superior systems in precision can be easily selected from the proposed class

locating an absolute center on graphs that are almost trees abstract physical models that exhibit a treelike graph structure frequently arise in telecommunication networks interstate highway systems and computer communication networks treelike graphs are characterized and properties related to the absolute center problem are analyzed that are preserved under two transformations of the graph utilizing these preserved properties a linear time algorithm is presented for the absolute center problem whenever the underlying graph is homeomorphic to a treelike 3 cactus graph

a logic of knowledge and justified assumptions abstract in this paper we define the logic gk of knowledge and justified assumptions gk is best understood as a formalization of autoepistemic reasoning processes that are more general than those in moore s autoepistemic logic and is formally defined via a modification of shoham s preference semantics we show that gk includes not only moore s autoepistemic logic but also reiter s default logic to our knowledge gk is the first complete semantic unification of the two logics similarly to circumscription gk is based on the notion of logical minimization and thus provides a bridge between circumscription and fixed point nonmonotonic logics an outstanding problem in nonmonotonic logics as an application of this bridge we propose a formalization of logic programs with negation as failure in circumscription

characteristic function games with restricted agent interactions in many real world settings the structure of the environment constrains the formation of coalitions among agents these settings can be represented by characteristic function games also known as coalitional games equipped with interaction graphs an interaction graph determines the set of all feasible coalitions in that a coalition c can form only if the subgraph induced over the nodes agents in c is connected our work analyzes stability issues arising in such environments by focusing on the core as a solution concept and by considering the coalition structure viewpoint that is without assuming that the grand coalition necessarily forms the complexity of the coalition structure core is studied over a variety of interaction graph structures of interest including complete graphs lines cycles trees and nearly acyclic graphs formally having bounded treewidth the related stability concepts of the least core and the cost of stability are also studied results are derived for the setting of compact coalitional games i e for games that are implicitly described via a compact encoding and where simple calculations on this encoding are to be performed in order to compute the payoff associated with any coalition moreover specific results are provided for compact games defined via marginal contribution networks an expressive encoding mechanism that received considerable attention in the last few years

nonmonotonic reasoning by inhibition nets abstract in this paper we will show that certain networks called inhibition nets may be regarded as cognitive agents drawing nonmonotonic inferences it will be proven that the system cl introduced by klm in artificial intelligence 44 1990 186 189 of nonmonotonic logic is both sound and complete with respect to the inferences drawn by finite hierarchical inhibition nets the latter class of inhibition nets is shown to correspond to the class of finite normal hierarchical logic programs concerning dynamics and also to the class of binary layered input driven artificial neural networks

solving np hard problems on graphs that are almost trees and an application to facility location problems description d une technique generale pour resoudre certains problemes de graphes np durs en un temps qui est exponentiel dans un parametre k defini comme le maximum sur tous les composants c non separables du graphe d un nombre de bords qui peut etre ajoute a l arbre pour produire c on donne un algorithme de temps de complexite o e 6r rh 27

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

improved addition for the logarithmic number system the logarithmic number system lns which offers a wide dynamic range with an independently choosable signal to noise ratio is discussed to realize addition voluminous lookup tables are needed a method is proposed to reduce the storage requirements of these tables by means of chebyshev approximation with unequally spaced partition points

knowledge and communication a first order theory this paper presents a theory of informative communications among agents that allows a speaker to communicate to a hearer truths about the state of the world the occurrence of events including other communicative acts and the knowledge states of any agent speaker hearer or third parties any of these in the past present or future and any logical combination of these including formulas with quantifiers we prove that this theory is consistent and compatible with a wide range of physical theories we examine how the theory avoids two potential paradoxes and discuss how these paradoxes may pose a danger when this theory are extended

an optimal algorithm for solving the 1 median problem on weighted 4 cactus graphs abstract the median problem has been extensively studied in the last three decades on general graphs the problem can be solved in o n 3 where n is the number of vertices in a graph for tree networks however more efficient algorithms can be devised to find the medians in o n in this paper we study weighted 4 cactus w4c graphs which provide a less restrictive network structure than trees and show that median problem can be solved just as efficiently on w4c graphs as on trees many examples are provided demonstrating the rudiments of our algorithm and a linear time complexity algorithm is developed

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

downward refinement and the efficiency of hierarchical problem solving abstract analysis and experiments have shown that hierarchical problem solving is most effective when the hierarchy satisfies the downward refinement property drp whereby every abstract solution can be refined to a concrete level solution without backtracking across abstraction levels however the drp is a strong requirement that is not often met in practice in this paper we examine the case when the drp fails and provide an analytical model of search complexity parameterized by the probability of an abstract solution being refinable our model provides a more accurate picture of the effectiveness of hierarchical problem solving we then formalize the drp in abstrips style hierarchies providing a syntactic test that can be applied to determine if a hierarchy satisfies the drp finally we describe an algorithm called highpoint that we have developed this algorithm builds on the alpine algorithm of knoblock in that it automatically generates abstraction hierarchies however it uses the theoretical tools we have developed to generate hierarchies superior to those generated by alpine this superiority is demonstrated empirically 2

finite precision rational arithmetic slash number systems fraction number systems characterized by fixed slash and floating slash formats are specified the structure of arithmetic over such systems is prescribed by the rounding obtained from best rational approximation multitiered precision hierarchies of both the fixed slash and floating slash type are described and analyzed with regards to their support of both exact rational and approximate real computation

axiomatic characterization of the agm theory of belief revision in a temporal logic since belief revision deals with the interaction of belief and information over time branching time temporal logic seems a natural setting for a theory of belief change we propose two extensions of a modal logic that besides the next time temporal operator contains a belief operator and an information operator the first logic is shown to provide an axiomatic characterization of the first six postulates of the agm theory of belief revision while the second stronger logic provides an axiomatic characterization of the full set of agm postulates

on composition of bounded recall plans abstract the article studies the ability of agents with bounded memory to execute consecutive composition of plans it gives an upper limit on the amount of memory required to execute the composed plans and shows that the limit cannot be improved furthermore the article shows that there are essentially no other universal properties of plans for bounded recall agents expressible through the relation there is a plan for an agent with a given memory size to navigate from one given set of states to another

state of the art location on networks a survey part ii exploiting tree network structure the discussion of the fundamental p center and p median problems in part i of this paper provides the basis for the work surveyed in part ii part ii deals with the minimax and minisum location problems with mutual communication location problems involving multiple objectives the distance constraints problem and problems involving the location of paths in addition convexity issues in network location problems are discussed virtually all of this work exploits network structure specifically it is based on the assumption that the network is a tree the conclusion section gives a brief discussion of the state of the art and of current trends in network location research

grounded fixpoints and their applications in knowledge representation in various domains of logic researchers have made use of a similar intuition that facts or models can be derived from the ground up they typically phrase this intuition by saying e g that the facts should be grounded or that they should not be unfounded or that they should be supported by cycle free arguments et cetera in this paper we formalise this intuition in the context of algebraical fixpoint theory we define when a lattice element x l is grounded for lattice operator o l l on the algebraical level we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory including supported minimal kripke kleene stable and well founded fixpoints on the logical level we investigate groundedness in the context of logic programming autoepistemic logic default logic and argumentation frameworks we explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields we investigate which existing semantics are grounded we study the novel semantics for these logics that is induced by grounded fixpoints which has some very appealing properties not in the least its mathematical simplicity and generality our results unveil a remarkable uniformity in intuitions and mathematics in these fields

on the complexity of cooperative solution concepts we study from a complexity theoretic standpoint the various solution concepts arising in cooperative game theory we use as a vehicle for this study a game in which the players are nodes of a graph with weights on the edges and the value of a coalition is determined by the total weight of the edges contained in it the shapley value is always easy to compute the core is easy to characterize when the game is convex and is intractable np complete otherwise similar results are shown for the kernel the nucleolus the e core and the bargaining set as for the von neumann morgenstern solution we point out that its existence may not even be decidable many of these results generalize to the case in which the game is presented by a hypergraph with edges of size k 2

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

conditional logics of normality a modal approach abstract several conditional theories of default reasoning have recently been proposed for the representation of statements about normal states of affairs or prototypical properties the natural semantics of these systems and their ability to reason about default rules make these approaches quite appealing we present a family of modal logics in which we define a conditional connective for statements of normality and examine its properties we also demonstrate that two of the most important conditional approaches are equivalent to fragments of our conditional logics of normality and to standard modal logics the approach we take is general enough to allow the expression of a number of different forms of defeasible reasoning and can be used to illustrate the relationship between these types of reasoning e g belief revision subjunctive and autoepistemic reasoning and our default logics this relationship is explored in a companion paper

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

pipelined computation of very large word length lns addition subtraction with polynomial hardware cost a novel pipelined method is proposed to compute the addition subtraction in very large word length logarithmic number system lns arithmetic digit parallel additive normalization and digit on line multiplicative normalization methods are adopted to compute the exponential and logarithmic functions respectively in lns addition subtraction these two methods can both be implemented in a pipelined and regular architecture the size of the required lookup tables is now proportional to a third order polynomial function instead of an exponential function of the word length the total size of the tables in a 32 bit lns unit is estimated to be less than 53 5 kbits and the total size of the table s in a 64 bit lns unit will be less than 471 kbits furthermore the hardware cost of the other circuits in the proposed lns unit is only proportional to the square of the word length this study also develops a simple leading zero bits prediction technique that can significantly enhance the precision in lns addition subtraction computation when compared to floating point arithmetic design our approach still suffers from large hardware cost and pipeline latency however the proposed approach has provided a theoretical advancement in the development of very large word length lns arithmetic

definability and commonsense reasoning abstract the definition of concepts is a central problem in commonsense reasoning many themes in nonmonotonic reasoning concern implicit and explicit definability implicit definability in nonmonotonic logic is always relative to the context the current theory of the world we show that fixed point equations provide a generalization of explicit definability which correctly captures the relativized context theories expressed within this logical framework provide implicit definitions of concepts moreover it is possible to derive these fixed points entirely within the logic

possible world semantics and autoepistemic reasoning abstract the possible world semantics of modal logic has been employed to study the nonmonotonic reasoning formalism moore s autoepistemic logic only kripke structure which is also known as a standard model has been used to represent the autoepistemic expansions of modal theories here we argue that the mode of autoepistemic reasoning which is formalized by autoepistemic logic is not necessarily associated with a standard model another model of the possible world semantics the minimal model is helpful in knowledge representation and belief reasoning in particular the minimal model can be used as a structure to represent all the autoepistemic expansions of a modal theory we extend the minimal model with standard model to deal with both knowledge and belief and introduce a null value called unknown to provide a refined model for knowledge and belief we also present a notion of epistemic base of basic sentences to identify the possible worlds in a minimal model by reformulating moore s autoepistemic logic with respect to epistemic base some reasonable modal theories that do not have any autoepistemic expansion will have generalized autoepistemic expansions

applying features of ieee 754 to sign logarithm arithmetic various features found in standard floating point arithmetic ieee 754 are examined in light of their appropriateness for sign logarithm arithmetic the emphasis is on a 32 b word size comparable to ieee 754 single precision although other word sizes are possible a multilayer sign logarithm format is considered the lowest layer similar to previous implementations would provide only normalized representations but would not provide representations for zero denormalized values infinities and nans the highest layer would provide most of the features found in ieee 754 including zeros denormalized values infinities and nans novel algorithms for implementing logarithmic denormalized arithmetic are presented simulation results show that the error characteristics of the proposed logarithmic denormalized arithmetic algorithms are similar to those of the denormalized floating point arithmetic in ieee 754

on embedding default logic into moore s autoepistemic logic abstract recently gottlob proved 2 that there does not exist a faithful modular translation of default logic into autoepistemic logic and presented a non modular translation gottlob s translation however is indirect it uses nonmonotonic logic n as an intermediate point quite complex and exploits sophisticated encoding of proof theory in autoepistemic formulas we provide a simpler and more intuitive non modular direct translation in addition our argument is purely model theoretic

reasoning with infinite stable models this paper illustrates extensively the theoretical properties the implementation issues and the programming style underlying finitary programs they are a class of normal logic programs whose consequences under the stable model semantics can be effectively computed despite the fact that finitary programs admit function symbols hence infinite domains and recursion from a theoretical point of view finitary programs are interesting because they enjoy properties that are extremely unusual for a nonmonotonic formalism such as compactness from the application point of view the theory of finitary programs shows how the existing technology for answer set programming can be extended from problem solving below the second level of the polynomial hierarchy to all semidecidable problems moreover finitary programs allow a more natural encoding of recursive data structures and may increase the performance of credulous reasoners

alternating time temporal logic temporal logic comes in two varieties linear time temporal logic assumes implicit universal quantification over all paths that are generated by the execution of a system branching time temporal logic allows explicit existential and universal quantification over all paths we introduce a third more general variety of temporal logic alternating time temporal logic offers selective quantification over those paths that are possible outcomes of games such as the game in which the system and the environment alternate moves while linear time and branching time logics are natural specification languages for closed systems alternating time logics are natural specification languages for open systems for example by preceding the temporal operator eventually with a selective path quantifier we can specify that in the game between the system and the environment the system has a strategy to reach a certain state the problems of receptiveness realizability and controllability can be formulated as model checking problems for alternating time formulas depending on whether or not we admit arbitrary nesting of selective path quantifiers and temporal operators we obtain the two alternating time temporal logics atl and atl atl and atl are interpreted over concurrent game structures every state transition of a concurrent game structure results from a choice of moves one for each player the players represent individual components and the environment of an open system concurrent game structures can capture various forms of synchronous composition for open systems and if augmented with fairness constraints also asynchronous composition over structures without fairness constraints the model checking complexity of atl is linear in the size of the game structure and length of the formula and the symbolic model checking algorithm for ctl extends with few modifications to atl over structures with weak fairness constraints atl model checking requires the solution of 1 pair rabin games and can be done in polynomial time over structures with strong fairness constraints atl model checking requires the solution of games with boolean combinations of buchi conditions and can be done in pspace in the case of atl the model checking problem is closely related to the synthesis problem for linear time formulas and requires doubly exponential time

arithmetic co transformations in the real and complex logarithmic number systems the real logarithmic number system which represents a value with a sign bit and a quantized logarithm can be generalized to create the complex logarithmic number system which replaces the sign bit with a quantized angle in a log polar coordinate system although multiplication and related operations are easy in both real and complex systems addition and subtraction are hard especially when interpolation is used to implement the system both real and complex logarithmic arithmetic benefit from the use of co transformation which converts an addition or subtraction from a region where interpolation is expensive to a region where it is easier two co transformations that accomplish this goal are introduced the first is an approximation based on real analysis of the subtraction logarithm the second is based on simple algebra that applies for both real and complex values and that works for both addition and subtraction

on the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent s rational beliefs on gradable propositions it has recently been shown that in the same way as autoepistemic logic generalizes answer set programming fuzzy autoepistemic logic generalizes fuzzy answer set programming as well besides being related to answer set programming autoepistemic logic is also closely related to several modal logics to investigate whether a similar relationship holds in a fuzzy logical setting we firstly generalize the main modal logics for belief to the setting of finitely valued ukasiewicz logic with truth constants k c and secondly we relate them with fuzzy autoepistemic logics moreover we show that the problem of satisfiability checking in these logics is np complete finally we generalize levesque s results on stable expansions belief sets and only knowing operators to our setting and provide a complete axiomatization for a logic of only knowing in the k c framework

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

on the computational complexity of coalitional resource games we study coalitional resource games crgs a variation of qualitative coalitional games qcgs in which each agent is endowed with a set of resources and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources we investigate and classify the computational complexity of a number of natural decision problems for crgs over and above those previously investigated for qcgs in general for example we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound i e a limit value for every resource is co np complete we then investigate the relationship between crgs and qcgs and in particular the extent to which it is possible to translate between the two models we first characterise the complexity of determining equivalence between crgs and qcgs we then show that it is always possible to translate any given crg into a succinct equivalent qcg and that it is not always possible to translate a qcg into an equivalent crg we establish some necessary and some sufficient conditions for a translation from qcgs to crgs to be possible and show that even where an equivalent crg exists it may have size exponential in the number of goals and agents of its source qcg

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

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

reasoning about coalitional games we develop investigate and compare two logic based knowledge representation formalisms for reasoning about coalitional games the main constructs of coalitional game logic cgl are expressions for representing the ability of coalitions which may be combined with expressions for representing the preferences that agents have over outcomes modal coalitional game logic mcgl is a normal modal logic in which the main construct is a modality for expressing the preferences of groups of agents for both frameworks we give complete axiomatisations and show how they can be used to characterise solution concepts for coalitional games we show that while cgl is more expressive than mcgl the former can only be used to reason about coalitional games with finitely many outcomes while mcgl can be used to reason also about games with infinitely many outcomes and is in addition more succinct we characterise the computational complexity of satisfiability for cgl and give a tableaux based decision procedure

semi logarithmic number systems we present a new class of number systems called semi logarithmic number systems that constitute a family of various compromises between floating point and logarithmic number systems this allows trade between the speed of the arithmetic operations and the size of the required tables we give arithmetic algorithms addition subtraction multiplication division for the semi logarithmic number systems and we compare these number systems to the classical floating point or logarithmic number systems