We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.

We study the problem of finding a basis for all rules admissible in the intuitionistic propositional logic IPC. The main result is Theorem 3.1 which gives a basis consisting of all rules in semi-reduced form satisfying certain specific additional requirements. Using developed technique we also find a basis for rules admissible in the logic of excluded middle law KC.

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.

The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and (...) GSc. (shrink)

We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.

This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a (...) negative solution. Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions. (shrink)

We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.

In this paper we study the admissible rules of intermediate logics. We establish some general results on extensions of models and sets of formulas. These general results are then employed to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.

Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic objects, for admissibility, the basic objects are sequent rules. Proof systems are defined here for admissible rules of classes of modal logics, including K4, S4, and (...) GL, and also Intuitionistic Logic IPC. With minor restrictions, proof search in these systems terminates, giving decision procedures for admissibility in the logics. (shrink)

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this (...) theorem–K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility. (shrink)

The main result of this paper is the following theorem: each modal logic extendingK4 having the branching property belowm and the effective m-drop point property is decidable with respect to admissibility. A similar result is obtained for intermediate intuitionistic logics with the branching property belowm and the strong effective m-drop point property. Thus, general algorithmic criteria which allow to recognize the admissibility of inference rules for modal and intermediate logics of the above kind are found. These criteria are applicable (...) to most modal logics for which decidability with respect to admissibility is known and to many others, for instance, to the modal logicsK4,K4.1,K4.2,K4.3,S4.1,S4.2,GL.2; to all smallest and greatest counterparts of intermediate Gabbay-De-Jong logicsD n; to all intermediate Gabbay-De-Jong logicsD n; to all finitely axiomatizable modal and intermediate logics of finite depth etc. Semantic criteria for recognizing admissibility for these logics are offered as well. (shrink)

This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is (...) class='Hi'>admissible. We prove that any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

If the Visser rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of the Visser rules are admissible is not known. In this paper we give a brief overview of results on admissible rules in the context of intermediate logics. We apply these results to some well-known intermediate (...) logics. We provide natural examples of logics for which the Visser rule are derivable, admissible but nonderivable, or not admissible. (shrink)

We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking (...) just unifiability of formulas with coefficients also works via verification of admissibility. (shrink)

Epistemic logics for subjects of bounded rationality are in effect nonnormal modal logics. Admissible rules are of interest in such logics. However, the usual methods for establishing admissibility employ Kripke models and are therefore inappropriate for nonnormal logics. This paper extends syntactic methods for a variety of rules and nonnormal logics. In doing so it answers a question asked by Chellas and Segerberg.

We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.

Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of (...) Visser's rules. We apply these results to some specific intermediate logics and obtain that Visser's rules form a basis for the admissible rules of, for example, De Morgan logic, and that Dummett's logic and the propositional Gödel logics do not have nonderivable admissible rules. (shrink)

The paper studies the admissibility of some cancellation rules in normal modal systems with the Brouwerian axiom. For example, KDB and KTB are proved to admit the following rule: if ⊢ ¬ and ⊢ ⋄α ≡ ⋄β then ⊢ ¬. Two notions of the preservation of validity by a rule on a frame are defined; on both, the preservation of validity by the preceding rule is shown not to be a first-order condition. A speculative connection is suggested with logics (...) of vagueness. (shrink)

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that a (...) rule is derivable in the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics. (shrink)

Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5n a basis for admissible rules and the form of all passive rules are (...) provided. (shrink)

Edmund Pellegrino and David Thomasma’s writings have had a worldwide impact on discourse about the philosophy of medicine, professionalism, bioethics, healthcare ethics, and patients’ rights. Given their works’ importance, it is surprising that commentators have ignored their admission of an unresolved and troubling dilemma and inconsistency in their theory. The purpose of this article is to identify and state what problems worried them and to consider possible solutions. It is argued that their dilemma stems from their concerns about how to (...) justify professional rules restricting colleagues from performing acts they view as direct, active, and formal killings, such as physician-assisted suicide, mercy killing, and abortion. It is further argued that their inconsistency is that they both assert and deny that professional colleagues should not use their moral or theological values to impose professional restrictions on other colleagues without adequate philosophical grounds. At risk are their arguments about the nature of an internal morality for medicine, a secular and multicultural basis for medical ethics, and a nonarbitrary way to determine what acts fall outside the ends of medicine. These are arguments they claim also apply to other healthcare professions. The article begins with a brief overview of their key positions to provide the context in which they make their admission. (shrink)

The paper deals with a temporal multi-agent logic TMAZ, which imitates taking of decisions based on agents' access to knowledge by their interaction. The interaction is modelled by possible communication channels between agents in special temporal Kripke/hintikka-like models. The logic TMAZ distinguishes local and global decisions-making. TMAZ is based on temporal Kripke/hintikka models with agents' accessibility relations defined on states of all possible time clusters C(i) (where indexes i range over all integer numbers Z). The main result provides a decision (...) algorithm for TMAZ (so, we prove that TMAZ is decidable). This algorithm also solves the satisfiability problem. In the final part of the paper, we consider the admissibility problem for inference rules in TMAZ, and show that this problem is decidable for TMAZ as well. (shrink)

We give a necessary and sufficient condition for any modal logic with fmp to inherit all inference rules admissible in S4. Using this condition we describe all tabular modal logics inheriting inference rules admissible for S4.

A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer the metatheoretical results to the original logic (e.g., [1, 6, 8, 18, 10, 12]). In the first-order modal case, on one hand we know that the Gentzenisation of the straightforward first-order extension of GL, the logic QGL, admits no cut elimination (if the rule is included as primitive; (...) or, if not included, then the rule is not admissible [1]). On the other hand the (cut-free) Gentzenisations of the first-order modal logics M3 and ML3 of [10, 12] do have cut as an admissible rule. The syntactic cut admissibility proof given in [18] for the Gentzenisation of the propositional provability logic GL is extremely complex, and it was the basis of the proofs of cut admissibility of the Gentzenisations of M3 and ML3, where the presence of quantifiers and quantifier rules added to the complexity and length of the proof. A recent proof of cut admissibility in a cut-free Gentzenisation of GL is given in [5] and is quite short and easy to read. We adapt it here to revisit the proofs for the cases of M3 and ML3, resulting to similarly short and easy to read proofs, only slightly complicated by the presence of quantification and its relevant rules. (shrink)

The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve (...) $\mathbf{t}$ . This calculus, $LT_\to^{\text{\textcircled{$\mathbf{t}$}}}$ , extends the consecution calculus $LT_{\to}^{\mathbf{t}}$ formalizing the implicational fragment of ticket entailment . We introduce two other new calculi as alternative formulations of $R_{\to}^{\mathbf{t}}$ . For each new calculus, we prove the cut theorem as well as the equivalence to the original Hilbert-style axiomatization of $R_{\to}^{\mathbf{t}}$ . These results serve as a basis for our positive solution to the long open problem of the decidability of $T_{\to}$ , which we present in another paper. (shrink)

Professor Imwinkelried has boldly attempted to justify the admissibility of normative ethical expertise in the face of a legal evidentiary rule requiring a scientific basis for expert testimony. Because ethical testimony is inherently unscientific, Professor Imwinkelried prudently focuses his analysis on circumstances where evidentiary requirements are less strict; those involving the legislative rather than adjudicative function of courts and those in which substantive law overrides normally rigorous evidentiary requirements. While both proposals may have merit and are thoughtful and creative, (...) Professor Imwinkelried ultimately fails to provide sufficient doctrinal support or persuasive rationale for his arguments.Professor Imwinkelrieds argument for the admissibility of “expert” normative ethical testimony has two parts. The major proposition is that, when courts are engaged in legislative functions, they should be permitted to consider all sources of information. The assumption that apparently underlies this proposition is that nothing limits courts’ exercise of legislative powers. (shrink)

Professor Imwinkelried has boldly attempted to justify the admissibility of normative ethical expertise in the face of a legal evidentiary rule requiring a scientific basis for expert testimony. Because ethical testimony is inherently unscientific, Professor Imwinkelried prudently focuses his analysis on circumstances where evidentiary requirements are less strict; those involving the legislative rather than adjudicative function of courts and those in which substantive law overrides normally rigorous evidentiary requirements. While both proposals may have merit and are thoughtful and creative, (...) Professor Imwinkelried ultimately fails to provide sufficient doctrinal support or persuasive rationale for his arguments.Professor Imwinkelrieds argument for the admissibility of “expert” normative ethical testimony has two parts. The major proposition is that, when courts are engaged in legislative functions, they should be permitted to consider all sources of information. The assumption that apparently underlies this proposition is that nothing limits courts’ exercise of legislative powers. (shrink)

The idea that ethics is a matter of personal feeling is a dogma widespread among medical students. Because emotivism is firmly rooted in contemporary culture, the authors think that focusing on personal feeling can be an important point of departure for moral education. In this contribution, they clarify how personal feelings can be a solid basis for moral education by focusing on the analysis of compassion by the French phenomenologist Emmanuel Housset. This leads to three important issues regarding ethics (...) education: the necessity of a continuous attention for and interpretation of the meaning of language, the importance of examining what aspect of “the other” touches one and what it is that evokes the urge to act morally and the need to relate oneself to the community, both to the medical community and to collectively formulated rules and laws. These issues can have a place in medical education by means of an ethical portfolio that supports students in their moral development. First, keeping a portfolio will improve their expression of the moral dimension of medical practice. Second, the effects of self-knowledge and language mastery will limit the pitfalls of emotivism and ethical subjectivism and will stimulate the inclination to really encounter the other. Third, it will show medical students from the start that their moral responsibility is more than following rules and that they are involved personally. (shrink)

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. (...) The book is basically self-contained and special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

The contraction-free sequent calculus G4 for intuitionistic logic is extended by rules following a general rule-scheme for nonlogical axioms. Admissibility of structural rules for these extensions is proved in a direct way by induction on derivations. This method permits the representation of various applied logics as complete, contraction- and cut-free sequent calculus systems with some restrictions on the nature of the derivations. As specific examples, intuitionistic theories of apartness and order are treated.

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

The authors argue that corporate philanthropy is far too important as a social instrument for good to depend on ethical egoism for its support. They claim that rule utilitarianism provides a more compelling, though not exclusive, moral foundation. The authors cite empirical and legal evidence as additional support for their claim.

Externalities are an important concept in economic theories of market failure, aiming to justify state regulation of the economy. This article explores the concept of externalities from a philosophical perspective. It criticizes the utilitarian nature of economic analyses of externalities, showing how they cannot take into account values like freedom and justice. It then develops the analogy between the concept of externalities and the 'harm principle' in political philosophy. It argues that the harm principle points to the need for a (...) theory of basic interests to judge when a harm is imposed. Similarly, externality analyses should use such a theory of basic interests as the basis for judgments about legitimate state intervention. This proposal is defended against objections, and illustrated with a case study of the US Supreme Court's ruling on the Affordable Care Act, which shows how the judicial reasoning implicitly interprets externalities in terms of basic interests. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 10.1 (2000) 75-80 [Access article in PDF] Bioethics Inside the Beltway: A New Basis for Allocating Livers for Transplant Robert M. Veatch The Department of Health and Human Services (DHHS) and the United Network for Organ Sharing (UNOS), the private organization with the government contract to manage the national organ transplant program, are in the midst of a protracted dispute over how livers (...) for transplant should be allocated. UNOS, which is based in Richmond, Virginia, has for many years set the national policy for allocating cadaver organs. UNOS had a policy that, in effect, gave healthy local recipients priority over much sicker, more urgent cases beyond the local level. In April of 1998, Donna Shalala, the Secretary of Health and Human Services, issued a regulation requiring that organs must be allocated according to uniform medical criteria and that organ sharing must take place over broad enough areas to ensure that organs can reach the patients who need them most. In effect, she sought to overturn the strict local priority in favor of a more uniform national list based on medical need or at least an approach that extended allocation beyond the strict locals-first approach.UNOS has put up great resistance, expressing a strong preference for retaining local priority even though doing so means some desperately sick people at more distant centers almost certainly will die for lack of organs. What sounds at first like a rather esoteric dispute over government regulation turns out to raise some fascinating issues involving questions of ethics and moral epistemology. The Background For several years, UNOS followed a policy of dividing all potential liver transplant recipients into four categories based on how urgently the person needed a transplant. Status 1 patients were the sickest, essentially those in intensive care. Status 2 patients were the next most ill-in the hospital, but not the ICU. Status 3 patients were ill enough to be at home, while Status 4 patients were still up and about. UNOS coordinates 62 local organ procurement organizations (OPOs), each serving a metropolitan area. These are grouped into 11 regions.The long-term allocation rule gave first priority to local Status 1 patients. If no Status 1 patient was available locally, rather than sending the organ to another OPO, it would be assigned to a Status 2 patient in the same OPO where the [End Page 75] organ was procured, then to a local Status 3 patient, and then to one at Status 4. Only if no patients could use the organ locally would it be "exported" to another OPO. It would then be offered to another OPO in the same region, starting once again with patients at the most urgent status. Only if no patients in the region could use the organ would it be offered outside the region. The effect of this policy was that in some cases quite well-off local patients could get priority over more distant patients who only had hours or days to live if they did not get transplanted. (It was because of this policy that Mickey Mantle-who was Status 2-got an organ so quickly. There were no other suitable Status 1 or 2 patients in the Dallas area. He did not have to compete with any of the thousands of liver transplant patients on the waiting lists beyond his local area.)The realization that critically ill patients beyond the local area were dying while healthy local patients got organs even though they still could wait for perhaps months or years led DHHS to issue its mandate. The goal was to get more organs to people who were in desperate need.The response at UNOS has been hostile. UNOS is made up primarily of representatives from the OPOs, which, in turn are often dominated by transplant surgeons. They did not like the idea that locally-procured organs were being shipped to other communities when they had their own patients who needed them.Spokespersons for this position offered two primary arguments. First, they believed that people would be more... (shrink)

Cardiopulmonary resuscitation is frequently performed on patients who, in retrospect, had a very low chance of survival. This is because all patients are ‘For cardiopulmonary resuscitation’ on admission to hospital by default, and delays occur before cardiopulmonary resuscitation can be ‘de-prescribed’. This article reviews the nature of potential harms caused by futile cardiopulmonary resuscitation, the reasons why de-prescription may be delayed, recent legal judgements relevant to timely do not attempt cardiopulmonary resuscitation decision making, and the possible detrimental effects of do (...) not attempt cardiopulmonary resuscitation discussions on end of life care. The moral and operational feasibility of a model in which informed consent must be obtained before cardiopulmonary resuscitation is attempted in some patient groups is then explored. (shrink)

The rule of rescue holds that special weight should be given to protecting the lives of assignable individuals in need, implying that less weight is given to considerations of cost-effectiveness. This is sometimes invoked as an argument for funding or reimbursing life-saving treatment in public healthcare even if the costs of such treatment are extreme. At first sight one might assume that an individualist approach to ethics—such as Scanlon’s contractualism—would offer a promising route to justification of the rule of rescue. (...) In this chapter I argue that contractualism cannot endorse the rule of rescue, whereas a collectivist approach that appeals to group solidarity would offer support for rescue cases. The argument, however, has its limitations, and though solidarity is of central concern in shaping public healthcare, there are good reasons for not endorsing the rule of rescue as a moral basis for allocating scarce resources in clinical care. (shrink)

We examine the sense in which logic is a priori, and explain how mathematical theories can be dichotomized non-trivially into analytic and synthetic portions. We argue that Core Logic contains exactly the a-priori-because-analytically-valid deductive principles. We introduce the reader to Core Logic by explaining its relationship to other logical systems, and stating its rules of inference. Important metatheorems about Core Logic are reported, and its important features noted. Core Logic can serve as the basis for a foundational program (...) that could be called Natural Logicism, an exposition of which will build on the (meta)logical ideas explained here. (shrink)

Heidegger has provided a profound account of human existence in terms of the to-be-da. Even though Heidegger disregarded its brain machine basis (and even though brain scientists disregard Heidegger), the issue of the Dasein's machine basis is raised by the empirically extremely well confirmed “supervenience” of the Dasein on the brain. Since the Turing machine will not do as basis for the Dasein, as Dreyfus has shown, contemporary functionalism cannot resolve the issue. Instead an “existential functionalism,” which (...) looks to some other kind of machine than the computer, is called for. A machine that continuously tunes filters on input and that detects any match between abstract properties of the input flux and filter specifications was considered. A match points to those tuning rules whose abstract conditions have been satisfied by input, and the rules thus selected are enabled to generate their own fulfillment through mechanisms that can presently be only speculated about. Such a machine cannot sustain direct perception but is “methodologically solipsistic.” At the most general level of description, the wet machine that provides a supervenience base for the Dasein is to be considered a “windowless monad.”. (shrink)

Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility (...) itself – for restricted cases, to show the problems arising in the course of study. (shrink)

The paper investigates admissible inference rules for the multi-modal logic LTK, which describes a combination of linear time and knowledge. This logic is semantically defined as the set of all ℒ.

The precautionary approach has been widely considered reasonable for many issues in environmental policy, including climate change. It has also been recognized, however, that standard formulations of the precautionary principle suffer from many difficulties. An influential strategy to avoid these difficulties is to formulate a narrow version of the principle on the basis of the maximin rule. Rawls proposed that following the maximin rule can be rational under certain conditions. Defenders of this strategy argue that these conditions are approximated (...) when it comes to issues like climate change. In the first part of this paper, I argue that the Rawlsian conditions do not establish the unique rationality of the maximin rule, hence the precautionary principle cannot be defended on its basis. When the Rawlsian conditions are approximated, other principles can also lead to reasonable choices. In particular, a prioritarian principle can capture the precautionary approach and serve a useful role in climate change policy. I develop this proposal in the second part. (shrink)

The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which (...) describe all tabular logics preserving admissibility: a tabular logic λ preserves all admissible rules for H iff 7λ has width not more than 2 and is not included in each λ. MSC: 03B55, 03B20. (shrink)